Current detecting apparatus and current detecting method

ABSTRACT

This invention provides a current detecting apparatus including three conductors disposed radially from a branch point such that they are branched, three hall devices disposed between conductors adjacent of the three conductors, and an operation processing circuit for detecting a current flowing through each of the three conductors based on an operation output obtained by a predetermined operation based on electric signals from the respective hall devices.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a current detecting apparatus fordetecting a current flowing through an electric circuit loaded on anapparatus such as automobile and a current detecting method, and moreparticularly to technology for improving detection accuracy for acurrent flowing through each branch conductor.

2. Description of The Related Art

Recently, with prevailing of, for example, electric car, hybrid car andthe like, the necessity of a current detecting apparatus for, forexample, charge/discharge control has been intensified. As such acurrent detecting apparatus, a current detecting apparatus which isinstalled in an electric connecting box for distributing currents from apower supply and detecting a current flowing through a conductorincorporated in the electric connecting box using an electromagnetictransducer has been well known. However, the current detecting apparatususing the electromagnetic transducer has such a problem that because aplurality of conductors are incorporated in the electric connecting box,an accurate current detection is impossible due to an interference ofmagnetic flux generated by a current flowing through other conductorthan the conductor in which a detection object current flows.

To solve such a problem, a current detecting apparatus for electric wirehas been disclosed in, for example, Japanese Patent ApplicationLaid-Open No. 63-63974. In this current detecting apparatus as shown inFIG. 1, a conductor B in which the detection object current I₁ flows isdisposed substantially at right angle to other conductor A and further,a magnetic core 1 a through which the conductor B passes is disposedsubstantially at the right angle to that conductor B.

With this structure, magnetic fields H₂ and H₃ generated by current I₂flowing through other conductor A are canceled in a magnetic core 1 aand only a magnetic field H₁ generated by a current I₁ flowing through aconductor B passes through the magnetic core 1 a. Thus, theelectromagnetic transducer 1 b placed in a gap of the magnetic core 1 adoes not receive an interference from other conductor B, the current I₁flowing through the conductor B can be detected accurately.

However, because this conventional current detecting apparatus forelectric wire employs the magnetic core, there are such problems thatits weight and occupied volume cannot be reduced beyond eachpredetermined level and production cost is high. Particularly, if aplurality of conductors through the detection object current flows arearranged in parallel, the same number of the magnetic cores arenecessary, so that the weight and occupied volume increase depending onthe number of the conductors and further the production cost isincreased.

On the other hand, for example, in automotive current connecting box,not only a plurality of conductors are arranged in parallel in somecase, but also a conductor is branched to a plurality of conductors inthe electric connecting box, so that it comes that those pluralconductors are disposed in parallel in other case.

SUMMARY OF THE INVENTION

An object of the present invention is to provide a current detectingapparatus capable of detecting a current flowing through each conductoreven if a plurality of the conductors are disposed together, bypositively using a condition including branch conductors provided in anelectric connecting box, the current detecting apparatus being capableof being reduced in its size and weight at a low cost. Another object ofthe present invention is to provide a current detecting method capableof detecting a current flowing through each conductor at a highsensitivity even if a plurality of the conductors are disposed together.

To achieve the above object, according to a first aspect of the presentinvention, there is provided a current detecting apparatus comprising: n(n: integer satisfying n≧3) conductors disposed so as to be branchedradially from a branch point; m (m: integer satisfying m≧2)electromagnetic transducers disposed between adjacent conductors of then conductors; and an operation processing circuit for detecting acurrent flowing through each of the n conductors based on an operatingoutput obtained from a predetermined operation based on an electricsignal from each of the m electromagnetic transducers.

According to the first aspect of the present invention, theelectromagnetic transducers are disposed on both sides of each of the nconductors. A current flowing through each conductor is detected bycarrying out a predetermined operation on an electric signal from thetwo electromagnetic transducers. In this case, each of the twoelectromagnetic transducers receives a magnetic flux produced by adifference between a current before branching and a current afterbranching. Thus, even if the current which is a detection object isconstant, the magnetic flux is converted electromagnetically. As aresult, a current flowing through each conductor can be detected with ahigh sensitivity even if it is small.

Because no magnetism collecting core is used in the first aspect (inprincipal, it is not necessary to use the magnetism collecting core),the size, weight and production cost of the current detecting apparatuscan be reduced. Particularly, this effect is remarkable in detecting acurrent in each branch route.

According to a second aspect of the invention, there is provided acurrent detecting apparatus according to the first aspect wherein the nconductors are disposed on a flat plane including the branch point andthe m electromagnetic transducers are disposed such that a magnetismsensitive surface of each thereof exists on the flat plane.

According to the second aspect, because n conductors and melectromagnetic transducers are disposed on the same plane, magneticflux generated by current flow through each conductor enters a magnetismsensitive surface of each electromagnetic transducer. As a result, inthe operation processing circuit, an electric signal from eachelectromagnetic transducer does not have to be corrected, so thatoperation on the operation processing circuit is simplified.

According to the third aspect, there is provided a current detectingapparatus according to the second aspect wherein the n is “3” while thethree conductors are disposed every 120° from the branch point on theflat plane in three directions; the m is “3” while the threeelectromagnetic transducers are disposed at the same distance fromadjacent conductors and at the same distance from the branch point; andthe operation processing circuit detects a current flowing through theconductor by obtaining a difference of electric signal between the twoelectromagnetic transducers sandwiching each conductor.

According to the third aspect, a current flowing through each conductoris detected by obtaining a difference of electric signal from twoelectromagnetic transducers sandwiching the conductor. In this case, oneelectromagnetic transducer receives a magnetic flux in a predetermineddirection generated by a current before branching and a current afterbranching, while the other electromagnetic transducer receives amagnetic flux in an opposite direction generated by the current beforebranching and the current after the branching. Thus, even if thedetecting object current is constant, it comes that a magnetic fluxthree times a magnetic flux generated by a current if there is no branchis converted electromagnetically. As a result, even if the currentflowing through each conductor is small, it can be detected at a highsensitivity.

Further, even if there is a disturbing magnetic flux near this currentdetecting apparatus, it is canceled by obtaining a difference ofelectric signal from the two electromagnetic transducers. As a result,even if other conductors are provided together, an influence from themis not received. Thus, a current flowing through each conductor can bedetected at a high sensitivity. Further, currents flowing through threeconductors can be detected at a high sensitivity using threeelectromagnetic transducers. Therefore, this current detecting apparatuscan be produced at a lower cost as compared to a current detectingapparatus for detecting a current flowing through a conductor with twoelectromagnetic transducers.

According to a fourth aspect of the present invention, there is provideda current detecting apparatus according to the second aspect where the nis “3” while the three conductors are disposed in three directions fromthe branch point on the flat plane such that an angle between the firstconductor and the second conductor is 90°, an angle between the secondconductor and the third conductor is 90° and an angle between the thirdconductor and the first conductor is 180°; the m is “4” while the firstelectromagnetic transducer is disposed at the same distance from thefirst conductor and the second conductor and at the same distance fromthe branch point, the second electromagnetic transducer is disposed atthe same distance from the second conductor and the third conductor andat the same distance from the branch point, the third electromagnetictransducer is disposed symmetrically with the second electromagnetictransducer with respect to the third conductor and at the same distancefrom the branch point, and the fourth electromagnetic transducer isdisposed symmetrically with the first electromagnetic transducer withrespect to the first conductor and at the same distance from the branchpoint; the operation processing circuit detects a current flowingthrough the conductor by obtaining a difference of electric signalbetween the four electromagnetic transducers sandwiching each conductor.

According to this fourth aspect, a current flowing through eachconductor is detected by obtaining a difference of electric signal fromthe electromagnetic transducers which sandwich each conductor. In thiscase, a current flowing through each of the first conductor, secondconductor and third conductor can be detected at a high sensitivity.

Further, because the disturbing magnetic flux existing near the currentdetecting apparatus can be canceled, the current flowing through eachconductor can be detected at a high accuracy. Further, because currentsflowing three conductors can be detected at a high sensitivity usingonly four electromagnetic transducers, this current detecting apparatuscan be produced at a lower cost than a current detecting apparatus fordetecting a current flowing through a conductor using twoelectromagnetic transducers.

According to a fifth aspect of the present invention, there is provideda current detecting apparatus according to the second aspect wherein then is “4” while the four conductors are disposed every 90° from thebranch point on the flat plane in four direction; the m is “4” while thefour electromagnetic transducers are disposed at the same distance fromadjacent two conductors and at the same distance from the branch point;and the operation processing circuit detects a current flowing throughthe conductor by obtaining a difference of electric signal among thefour electromagnetic transducers sandwiching each conductor.

According to the fifth aspect of the present invention, a currentflowing through each conductor can be detected at a high sensitivity byobtaining a difference of electric signal from four electromagnetictransducers which sandwich each conductor.

Because the disturbing magnetic flux existing near the current detectingapparatus is canceled, a current flowing through each conductor can bedetected at a high accuracy. Further, because currents flowing throughthe four conductors can be detected at a high sensitivity using onlyfour electromagnetic transducers, the current detecting apparatus can beproduced at a lower cost than a current detecting apparatus fordetecting a current flowing through a conductor using twoelectromagnetic transducers.

According to a sixth aspect of the present invention, there is provideda current detecting apparatus according to the first aspect wherein then conductors are disposed on three-dimensional axes perpendicular toeach other with the branch point as a home position and the melectromagnetic transducers are disposed such that magnetism sensitivesurfaces thereof exist on a flat plane including two axes of the threeaxes.

According to this sixth aspect, the n conductors are disposed thethree-dimensional axes perpendicular to each other with the branch pointas a home position and m electromagnetic transducers are disposed suchthat the magnetism sensitive surfaces thereof exist on the same planeincluding two axes of the three axes. Thus, the magnetic flux generatedby current flow into each conductor existing on the same plane entersthe magnetism sensitive surface of each electromagnetic transducervertically. As a result, an electric signal from each electromagnetictransducer becomes accurate in the operation processing circuit, so thatoperation in the operation processing circuit is simplified.

According to a seventh aspect of the present invention, there isprovided a current detecting apparatus according to the sixth aspectwherein the n is “3” while the three conductors are disposed in threedirections of the three axes; the m is “3” while the firstelectromagnetic transducer is disposed at the same distance from thefirst conductor and the second conductor existing on the flat plane andat the same distance from the branch point, the second electromagnetictransducer is disposed symmetrically with the first electromagnetictransducer with respect to the second conductor and at the same distancefrom the branch point and the third electromagnetic transducer isdisposed symmetrically with the first electromagnetic transducer withrespect to the first conductor and at the same distance from the branchpoint; and the operation processing circuit detects a current flowingthrough each conductor of the first-third conductor by obtaining adifference of electric signal between three electromagnetic transducerssandwiching each of the first conductor and the second conductorexisting on the flat plane.

According to the seventh aspect, a current flowing through thefirst-third conductors is detected by obtaining a difference of electricsignal from the three electromagnetic transducers which sandwich eachconductor of the first conductor and the second conductor existing onthe flat plane.

Further, even if the disturbing magnetic flux exists near this currentdetecting apparatus, it is canceled by obtaining a difference ofelectric signal from the three electromagnetic transducers. As a result,even if other conductors are provided together, an influence therefromis not received. Thus, a current flowing through each conductor can bedetected. Further, currents flowing through the three conductors can bedetected at a high sensitivity using only three electromagnetictransducers. Thus, this current detecting apparatus can be produced at alower cost than a current detecting apparatus for detecting a currentflowing through a conductor using two electromagnetic transducers.

According to an eighth aspect of the present invention, there isprovided a current detecting apparatus according to the sixth aspectwherein the n is “4” while the four conductors are disposed on the threeaxes and a negative direction axis of one of the three axes; the m is“4” while the first-fourth electromagnetic transducers are disposed on aflat plane including two axes of the three axes and the negativedirection axes; the first electromagnetic transducer and the secondelectromagnetic transducer are disposed at the same distance from thefirst conductor which is one of the first-third conductors existing onthe flat plane and at the same distance from the branch point, the thirdelectromagnetic transducer is disposed symmetrically with the secondelectromagnetic transducer with respect to the second conductor and atthe same distance from the branch point, and the fourth electromagnetictransducer is disposed symmetrically with the third electromagnetictransducer with respect to the third conductor and at the same distancefrom the branch point; and the operation processing circuit detects acurrent flowing through each conductor of the first-fourth conductors byobtaining a difference of electric signal between the fourelectromagnetic transducers sandwiching each conductor of thefirst-third conductors existing on the flat plane.

According to the eighth aspect, a current flowing through each of thefirst-fourth conductors is detected by obtaining a difference ofelectric signal from the four electromagnetic transducers which sandwicheach conductor of the first-third conductors existing on the flat plane.

Further, the disturbing magnetic flux existing near this currentdetecting apparatus is canceled in the same way as the seventh aspect.Thus, a current flowing through each conductor can be detected. Further,currents flowing through the four conductors can be detected at a highsensitivity using only four electromagnetic transducers. Thus, thiscurrent detecting apparatus can be produced at a lower cost than acurrent detecting apparatus for detecting a current flowing through aconductor using two electromagnetic transducers.

According to a ninth aspect of the present invention, there is provideda current detecting apparatus according to the third-eighth aspectwherein the m electromagnetic transducers are disposed such that themagnetism sensitive surfaces thereof are directed in the same direction.

According to this ninth aspect, because the m electromagnetictransducers are disposed such that the respective magnetism sensitivesurfaces are directed in the same direction, the electric signal fromeach of the electromagnetic transducer can be handled easily in theoperation processing circuit, so that operation in the operationprocessing circuit is facilitated.

According to a tenth aspect of the present invention, there is provideda current detecting method comprising: disposing n (n: integersatisfying n≧3) conductors so as to be branched radially from a branchpoint; disposing m (m: integer satisfying m≧2) electromagnetictransducers between adjacent conductors of the n conductors; anddetecting a current flowing through each of the n conductors based on anoperating output obtained from a predetermined operation based on anelectric signal from each of the m electromagnetic transducers.According to the tenth aspect, the same operation and effect as thefirst aspect are exerted.

According to an eleventh aspect of the present invention, the nconductors are disposed on a flat plane including the branch point andthe m electromagnetic transducers are disposed such that a magnetismsensitive surface of each thereof exists on the flat plane. According tothe eleventh aspect, the same operation and effect as the second aspectare exerted.

According to a twelfth aspect of the present invention, there isprovided a current detecting method comprising: while the n is “3”,disposing the three conductors every 120° from the branch point on theflat plane in three directions; while the m is “3”, disposing the threeelectromagnetic transducers at the same distance from adjacentconductors and at the same distance from the branch point; and detectinga current flowing through the conductor by obtaining a difference ofelectric signal between the two electromagnetic transducers sandwichingeach conductor. According to the twelfth aspect, the same operation andeffect as the third aspect are exerted.

According to a thirteenth aspect of the present invention, there isprovided a current detecting method according to the eleventh aspectcomprising: while the n is “3”, disposing the three conductors in threedirections from the branch point on the flat plane such that an anglebetween the first conductor and the second conductor is 90°, an anglebetween the second conductor and the third conductor is 90° and an anglebetween the third conductor and the first conductor is 180°; while the mis “4”, disposing the first electromagnetic transducer at the samedistance from the first conductor and the second conductor and at thesame distance from the branch point, disposing the secondelectromagnetic transducer at the same distance from the secondconductor and the third conductor and at the same distance from thebranch point, disposing the third electromagnetic transducersymmetrically with the second electromagnetic transducer with respect tothe third conductor and at the same distance from the branch point, anddisposing the fourth electromagnetic transducer symmetrically with thefirst electromagnetic transducer with respect to the first conductor andat the same distance from the branch point; and detecting a currentflowing through the conductor by obtaining a difference of electricsignal between the four electromagnetic transducers sandwiching eachconductor. According to this thirteenth aspect, the same operation andeffect as the fourth aspect are exerted.

According to a fourteenth aspect of the present invention, there isprovided a current detecting method according to the eleventh aspectwherein the n is “4” while the four conductors are disposed every 90°from the branch point on the flat plane in four direction; the m is “4”while the four electromagnetic transducers are disposed at the samedistance from adjacent two conductors and at the same distance from thebranch point; and a current flowing through the conductor is detected byobtaining a difference of electric signal among the four electromagnetictransducers sandwiching each conductor. According to the fourteenthaspect, the same operation and effect as the fifth aspect are exerted.

According to a fifteenth aspect of the present invention, there isprovided a current detecting method wherein the n conductors aredisposed on three-dimensional axes perpendicular to each other with thebranch point as a home position and the m electromagnetic transducersare disposed such that magnetism sensitive surfaces thereof exist on aflat plane including two axes of the three axes. According to thisfifteenth aspect, the same operation and effect as the sixth aspect areexerted.

According to a sixteenth aspect of the present invention, there isprovided a current detecting method wherein the n is “3” while the threeconductors are disposed in three directions of the three axes; the m is“3” while the first electromagnetic transducer is disposed at the samedistance from the first conductor and the second conductor existing onthe flat plane and at the same distance from the branch point, thesecond electromagnetic transducer is disposed symmetrically with thefirst electromagnetic transducer with respect to the second conductorand at the same distance from the branch point and the thirdelectromagnetic transducer is disposed symmetrically with the firstelectromagnetic transducer with respect to the first conductor and atthe same distance from the branch point; and a current flowing througheach conductor of the first-third conductor is detected by obtaining adifference of electric signal between three electromagnetic transducerssandwiching each of the first conductor and the second conductorexisting on the flat plane. According to this sixteenth aspect, the sameoperation and effect as the seventh aspect are exerted.

According to a seventeenth aspect of the present invention, there isprovided a current detecting method wherein the n is “4” while the fourconductors are disposed on the three axes and a negative direction axisof one of the three axes; the m is “4” while the first-fourthelectromagnetic transducers are disposed on a flat plane including twoaxes of the three axes and the negative direction axes; the firstelectromagnetic transducer and the second electromagnetic transducer aredisposed at the same distance from the first conductor which is one ofthe first-third conductors existing on the flat plane and at the samedistance from the branch point, the third electromagnetic transducer isdisposed symmetrically with the second electromagnetic transducer withrespect to the second conductor and at the same distance from the branchpoint, and the fourth electromagnetic transducer is disposedsymmetrically with the third electromagnetic transducer with respect tothe third conductor and at the same distance from the branch point; anda current flowing through each conductor of the first-fourth conductorsis detected by obtaining a difference of electric signal between thefour electromagnetic transducers sandwiching each conductor of thefirst-third conductors existing on the flat plane. According to theseventeenth aspect, the same operation and effect as the eighth aspectare exerted.

According to an eighteenth aspect of the present invention, there isprovided a current detecting method wherein the m electromagnetictransducers are disposed such that the magnetism sensitive surfacesthereof are directed in the same direction.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram for explaining an example of a conventional currentdetecting apparatus;

FIG. 2 is a plan view showing a structure of a sensor portion of acurrent detecting apparatus according to a first embodiment of thepresent invention;

FIG. 3 is a block diagram showing a structure of the current detectingapparatus including a sensor portion shown in FIG. 2;

FIG. 4 is a structure diagram of an electric circuit in case where thecurrent detecting apparatus of the first embodiment of the presentinvention is applied to automobile;

FIG. 5 is a diagram showing a structure of an experimental circuit usedin experiment for verifying an operation principle and detectingcharacteristic of the current detecting apparatus according to the firstembodiment of the present invention;

FIG. 6 is a diagram showing a measurement result and computation resultin a condition that no disturbing magnetic flux exists in theexperimental circuit shown in FIG. 5;

FIG. 7 is a diagram showing a measurement result and computation resultin a condition that disturbing magnetic flux exists in the experimentalcircuit shown in FIG. 5;

FIG. 8 is a diagram showing a relation between the current I₁ flowingthrough a first conductor obtained by the experimental circuit shown inFIG. 5 and “S₂−S₃” obtained by computation;

FIG. 9 is a diagram showing a relation between the current I₂ flowingthrough a second conductor obtained by the experimental circuit shown inFIG. 5 and “S₁−S₂” obtained by computation;

FIG. 10 is a diagram showing a relation between the current I₃ flowingthrough a third conductor obtained by the experimental circuit shown inFIG. 5 and “S₁−S₃” obtained by computation;

FIG. 11 is a plan view showing a structure of a sensor portion of thecurrent detecting apparatus according to the second embodiment of thepresent invention;

FIG. 12 is a block diagram showing a structure of a computation controlcircuit in the current detecting apparatus shown in FIG. 11;

FIG. 13 is a plan view showing a structure of the sensor portion of thecurrent detecting apparatus according to a third embodiment of thepresent invention;

FIG. 14 is a block diagram showing a structure of the computationcontrol circuit in the current detecting apparatus shown in FIG. 13;

FIG. 15 is a perspective view showing a structure of the sensor portionof the current detecting apparatus according to a fourth embodiment ofthe present invention;

FIG. 16 is a block diagram showing a structure of the computationcontrol circuit of the current detecting apparatus shown in FIG. 15;

FIG. 17 is a perspective view showing a structure of the sensor portionof the current detecting apparatus according to a fifth embodiment ofthe present invention;

FIG. 18 is a block diagram showing a structure of the computationcontrol circuit of the current detecting apparatus shown in FIG. 17;

FIG. 19 is a plan view showing a structure of the sensor portion of thecurrent detecting apparatus according to a tenth embodiment of thepresent invention;

FIG. 20 is a diagram for explaining a magnetic field received by a firsthall device of the current detecting apparatus shown in FIG. 19 from acurrent flowing through the first conductor;

FIG. 21 is a diagram for explaining a magnetic field received by thefirst hall device of the current detecting apparatus shown in FIG. 19from a current flowing through the third conductor;

FIG. 22 is a diagram showing changes of sensitivity with respect tochanges of angle formed between the second conductor and the thirdconductor in the current detecting apparatus shown in FIG. 19;

FIG. 23 is a plan view showing a structure of the sensor portion of thecurrent detecting apparatus according to an eleventh embodiment of thepresent invention;

FIG. 24 is a diagram showing a first setting example for an angle formedbetween two conductors of the first-third conductors in the currentdetecting apparatus shown in FIG. 23;

FIG. 25 is a diagram showing a second setting example for an angleformed between two conductors of the first-third conductors in thecurrent detecting apparatus shown in FIG. 23;

FIG. 26 is a diagram showing a third setting example for an angle formedbetween two conductors of the first-third conductors in the currentdetecting apparatus shown in FIG. 23; and

FIG. 27 is a diagram showing a fourth setting example for an angleformed between two conductors of the first-third conductors in thecurrent detecting apparatus shown in FIG. 23.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The current detecting apparatus and current detecting method accordingto an embodiment of the present invention will be described withreference to the accompanying drawings. Like reference numerals areattached to the same components in respective embodiments fordescription thereof.

First Embodiment

The first embodiment is an example in which n of the present inventionis “3” and m is “3”. FIG. 2 is a plan view showing a structure of thecurrent detecting apparatus according to the first embodiment of thepresent invention. This sensor portion is comprised of a conductor 10, afirst hall device 21, a second hall device 22 and a third hall device23. Usually, these components are incorporated in an electric connectingbox. In the first embodiment, no magnetism collecting core is used.

The conductor 10 is comprised of the first conductor 11, secondconductor 12 and third conductor 13 disposed in three directions from abranch point O every 120° as shown in FIG. 2. The first conductor 11,second conductor 12 and third conductor 13 correspond to n conductors ofthe present invention. Ends of the respective conductors are connectedat the branch point O.

In the meantime, the conductor 10 may be composed by connecting ends ofthe three separate conductors, namely, the first conductor 11, secondconductor 12 and third conductor 13 at the branch point O and instead byforming integrally the first conductor 11, second conductor 12 and thirdconductor 13. Further, it is also permissible to compose this conductor10 by forming a wiring pattern having three branch routes including thefirst conductor 11, second conductor 12 and third conductor 13 on asubstrate.

The first hall device 21, second hall device 22 and third hall device 23correspond to m electromagnetic transducers of the present invention.Each hall device generates a voltage (hall voltage) signal correspondingto a density of magnetic flux entering its magnetism sensitive surface(magnetic flux detecting surface). A predetermined current is suppliedto each hall device through a lead (not shown) and the voltage signalgenerated in each hall device is fetched out through a lead (not shown).

Positions where the respective hall devices are disposed are determinedas follows. That is, the first hall device 21 is disposed between thefirst conductor 11 and the second conductor 12 and at the same distancefrom these conductors. The second hall device 22 is disposed between thesecond conductor 12 and the third conductor 13 and at the same distancefrom these conductors. The third hall device 23 is disposed between thethird conductor 13 and the first conductor 11 and at the same distancefrom these conductors. The respective hall devices are disposed at thesame distance from the branch point and near the branch point. Themagnetism sensitive surfaces of the respective hall devicessubstantially coincide with the plane including the branch point O andare disposed such that they are directed in the same direction.

Next, an operation of the sensor portion of the current detectingapparatus according to the first embodiment of the present inventionhaving such a structure will be described.

Assume that the magnetism sensitive surface of each hall device isdirected from a paper face toward yourself. Further assume that acurrent I₁ flows from the branch point O to its end in the firstconductor 11, a current I₂ flows from the end to the branch point O inthe second conductor 12 and a third current I₃ flows from the branchpoint O to the end in the third conductor I₃. The direction of currentflow mentioned here is just an example and it is not limited to theabove described one but any direction. Because the respective halldevices are disposed near each other and the magnetism sensitivesurfaces of the respective hall devices are directed to the samedirection, it is assumed that the respective magnetism sensitivesurfaces receive disturbing magnetic flux n equally.

If magnetic flux entering a magnetism sensitive surface of each of halldevices disposed on both sides of a conductor i when a current Ii flowsto the conductor i (i=1, 2, 3) is Ii and magnetic flux going out of themagnetism sensitive surface is f(I_(i)), total magnetic flux B₁ receivedby a magnetism sensitive plane of the first hall device 21 is“B₁=−f(I₁)−f(I₂) +n”. Total magnetic flux B₂ received by the magnetismsensitive surface of the second hall device 22 is “B₂=f(I₂)+f(I₃)+n.Total magnetic flux B₃ received by the magnetism sensitive surface ofthe third hall device 23 is “B₃=−f(I₃)+f(I₁)+n”.

Now, if “B₂−B₁” is calculated, it comes that “B₂−B₁=f(I₂)+f(I₃)+n−{−f(I₁)−f(I₂)+n}=f(I₁)+2*f(I₂)+f(I₃)”. Because “I₁+I₃=I₂ “for thereason of Kirchhoff formula, “B₂−B₁=3*f(I₂)” is obtained.

This “B₂−B₁=3*f(I₂)” is understood as follows. That is, if a current I₂flows through the second conductor 12, the magnetism sensitive surfaceof the first hall device 21 and the magnetism sensitive surface of thesecond hall device 22 receive magnetic flux of the same size and inopposite direction. If branch currents I₁ and I₃ flow to the firstconductor 11 and third conductor 13, the magnetism sensitive surface ofthe first hall device 21 and the magnetism sensitive surface of thesecond hall device 22 receive magnetic flux corresponding to the size ofeach branch current and in opposite direction to each other.

Thus, if subtraction is carried out between magnetic flux received bythe magnetism sensing plane of the first hall device 21 and magneticflux received by the magnetism sensitive surface of the second halldevice 22, this is the same as when magnetic flux which is three times amagnetic flux generated when the current I₂ flows through the secondconductor 12. Further, because the subtraction is carried out,disturbing magnetic flux n received by the magnetism sensitive surfaceof the first hall device 21 and the disturbing magnetic flux n receivedby the magnetism sensitive plane of the second hall device 22 kill eachother.

Next, if “B₃−B₁” is calculated, it comes that“B₃−B₁=−f(I₃)+f(I₁)+n−{−f(I₁)−f(I₂)+n}=2*f(I₁)+f(I₂)−f(I₃)”. Because“f(I₁)=f(I₂)−f(I₃)” is established for the reason of Kirchhoff formula,“B₃−B₁=3*f(I₁) is obtained.

Further, if “B₂−B₃” is calculated, it comes that“B₂−B₃=f(I₂)+f(I₃)+n−{−f(I₃)+f(I₁)+n}=2*f(I₃)+f(I₂)+f(I₁)”. Because“f(I₃)=f(I₂)−f(I₁)” is established for the reason of Kirchhoff formula,“B₂−B₃=3*f(I₃)” is obtained.

When the current I₂ flowing through the second conductor 12, current I₁flowing through the first conductor 11 and current I₃ flowing throughthe third conductor 12 are detected, each result of computation of“B₂−B₁”, “B₃−B₁” and “B₂−B₃” becomes equal to generating of a magneticflux which is three times a magnetic flux generated when a current flowsthrough each conductor. Further, because the disturbing magnetic fluxcan be canceled, a current can be detected highly accurately. Further,because all the hall devices are disposed near the branch point O, errorfactors such as temperature drift are canceled also.

FIG. 3 is a block diagram showing the structure of the current detectingapparatus containing the above described sensor portion. In this currentdetecting apparatus, the sensor portion is comprised of the conductor10, first hall device 21, second hall device 22 and third hall device 23and further, an operation processing circuit 30 is added thereto. Theoperation processing circuit 30 is comprised of first operationamplifier 31, second operation amplifier 32 and third operationamplifier 33. An output from the operation processing circuit 30 issupplied to, for example, a central processing unit (hereinafterreferred to as CPU40).

The first operation amplifier 31 carries out operation equivalent to“−(B₃−B₁)”. A noninverting input terminal (+) of this first operationamplifier 31 is connected to the first hall device 21 and a noninvertinginput terminal (−) is connected to the third hall device 23 and anoutput terminal is connected to the CPU 40. Thus, the first operationamplifier 31 subtracts a voltage signal VB₃ corresponding to themagnetic flux B₃ from a voltage signal VB₁ corresponding to the magneticflux B₁ and supplies that result of subtraction to the CPU 40 as a firstdetection signal DT₁ indicating the magnitude of the current I₁. Becausethis first detection signal DT₁ is similar to a signal obtained byelectromagnetically converting a magnetic flux 3*f(I₁) which is threetimes a magnetic flux f(I₁) generated by only the current I₁, thecurrent I₁ flowing through the first conductor 11 can be detected at ahigh sensitivity. In an example shown in FIG. 3, the first detectionsignal DT₁ is obtained as a negative value.

The second operation amplifier 32 carries out operation corresponding to“B₂−B₁”. The noninverting input terminal (+) of this second operationamplifier 32 is connected to the second hall device 22, the noninvertinginput terminal (−) is connected to the first hall device 21 and the anoutput terminal is connected to the CPU 40. Therefore, the secondoperation amplifier 32 subtracts the voltage signal VB₁ corresponding tothe magnetic flux B₁ from the voltage signal VB₂ corresponding to themagnetic flux B₂. The subtraction result is supplied to the CPU 40 asthe second detection signal DT₂ indicating the magnitude of the currentI₂. Because this second detection signal DT₂ is similar to a signalobtained by electromagnetically converting a magnetic flux 3*f(I₂) whichis three times a magnetic flux f(I₂) generated by only the current I₂,the current I₂ flowing through the second conductor 12 can be detectedat a high sensitivity. Meanwhile, in an example shown in FIG. 3, thesecond detection signal DT₂ is obtained as a positive value.

The third operation amplifier 33 carries out operation corresponding to“B₂−B₃”. An noninverting input terminal (+) of this third operationamplifier 33 is connected to the third hall device 32, a noninvertinginput terminal (−) is connected to the second hall device 22 and anoutput terminal is connected to the CPU 40. Therefore, the thirdoperation amplifier 33 subtracts a voltage signal VB₃ corresponding tothe magnetic flux B₃ from a voltage signal VB₂ corresponding to themagnetic flux B₂. Its subtraction result is supplied to the CPU 40 asthe third detection signal DT₃ indicating the magnitude of the currentI₃. Because this third detection signal DT₃ is similar to a signalobtained by electromagnetically converting a magnetic flux 3*f(I₃) whichis three times a magnetic flux f(I₃) generated by only the current I₃,the current I₃ flowing through the third conductor 13 can be detected ata high sensitivity. Meanwhile, in an example shown in FIG. 3, the thirddetection signal DT₃ is obtained as a positive value.

The CPU 40 receives the first detection signal DT₁ from the firstoperation amplifier 31, the second detection signal DT₂ from the secondoperation amplifier 32 and the third detection signal DT₃ from the thirdoperation amplifier 33, and determines the magnitudes of currentsflowing through the first conductor 11, second conductor 12 and thirdconductor 13 and if necessary, drives a current circuit breaker or thelike.

Next, an example of a structure of an electric circuit when the abovedescribed current detecting apparatus is applied to automobile will bedescribed with reference to FIG. 4. This electric circuit is composed ofthe above described current detecting apparatus (sensor portion andoperation processing circuit 30), control circuit 40, generator 41,battery 42 stator 43 and load 44. Then, the first conductor 11 of thecurrent detecting apparatus is connected to the battery 42, the secondconductor 12 is connected to the generator 41 and the third conductor 13is connected to the load 44. A stator 43 controls conduction/shut-downbetween the battery 42 and the first conductor 11.

The control circuit 40 is comprised of the CPU 40 as indicated in FIG.3. This control circuit 40 judges a current condition of the electriccircuit according to the first detection signal DT₁, second detectionsignal DT₂ and third detection signal DT₃ from the operation processingcircuit 30 and drives the generator 41 as required.

The generator 41 generates power corresponding to a control signal fromthe control circuit 40. A current generated by this generator 41 issupplied to the battery 42 and load 44 through the second conductor 12.The battery 42 supplies a discharging current to the load 44 so as todrive the load 44 and at the same time, is supplied with a chargingcurrent from the generator 41 so that it is charged. The load 44comprises, for example, head lamp, wiper and the like.

By evaluating the first detection signal DT₁, second detection signalDT₂ and third detection signal DT₃ from the operation processing circuit30 totally, the electric circuit of automobile having such a structureis capable of instructing an optimal power generation amount to thegenerator 41 corresponding to an operation condition of the load 44 anda charging condition of the battery 42.

Next, to verify that the operation principle of the current detectingapparatus having such a structure is right and investigate a detectioncharacteristic thereof, the inventor of the present invention carriedout the following experiment. That result is shown below.

FIG. 5 shows a circuit used for this experiment. In this experimentalcircuit, a current from the power supply E is inputted to the thirdconductor 13 of the sensor portion through a resistor R. Then, thecurrent I₃ inputted to this third conductor 13 is divided to the currentI₁ flowing through the first conductor 11 and the current I₂ flowingthrough the second conductor 12. The current I₁ flowing through thefirst conductor 11 returns to the power supply E through the load LOAD1and the current I₂ flowing through the second conductor 12 returns tothe power supply E through the load LOAD2.

As the loads LOAD1 and LOAD2, loads capable of setting a flowing currentwas used. While changing current flowing through the loads LOAD1 andLOAD2, a current flowing through the third conductor 13 and voltage atthat time, and respective output voltages at the first hall device S₁,second hall device S₂ and third hall device S₃ were measured. Then, adifference between an output of the second hall device S₂ and output ofthe third hall device S₃, “S₂−S₃”, a difference between an output of thefirst hall device S₁ and output of the second hall device S₂, “S₁−S₂”and a difference between an output of the first hall device S₁ and thirdhall device S₃, “S₁−S₃” are obtained by calculation. Further, adisturbing magnetic field n was generated by bringing a magnet near thesensor portion. The magnetism sensing plane of each hall device uponexperiment was inverted with respect to the magnetism sensitive surfaceof the hall device shown in FIGS. 2, 3.

FIG. 6 shows a result of measurement carried out without the disturbingmagnetic flux and a result of computation. FIG. 7 is a diagram showing aresult of measurement carried out with the disturbing magnetic fluxapplied and a result of computation.

FIG. 8 shows a relation between the current I₁ flowing through the firstconductor 11 and “S₂−S₃” obtained by computation. FIG. 8A shows a casewhere the disturbing magnetic flux n does not exist and FIG. 8B shows acase where the disturbing magnetic flux n exists. FIG. 9 shows arelation between the current I₂ flowing through the second conductor 12and “S₁−S₂” obtained by computation. FIG. 12A shows a case where thedisturbing magnetic flux n does not exist and FIG. 12B indicates a casewhere the disturbing magnetic flux n exists. FIG. 10 shows a relationbetween the current I₃ flowing through the second conductor 13 and“S₁−S₃” obtained by computation. FIG. 13A shows a case where thedisturbing magnetic flux n does not exist and FIG. 13B indicates a casewhere the disturbing magnetic flux n exists.

As for an output of each hall device, if referring to FIG. 6, an outputsignal S₁ from the first hall device 21 is 16 mA under currentI₁(LOAD1)=30 A and current I₂(LOAD2)=0 A in case of No. 5 and an outputsignal S3 form the third hall device 23 is 19 mA under currentI₂(LOAD2)=30 A and current I₁(LOAD1)=0 A in case of No. 8. As a result,when the disturbing magnetic field n does not exist, it is evident thatcurrent detection capacity of a hall device when supplied power is notdivided is 16-19 mA for every 30 A.

Looking at a result of computation when 30 A flowed as the current I₁,computation signal S₂−S₃ is −56 mA under current I₁(LOAD1)=30 A andcurrent I₂(LOAD2)=30 A in case of No. 4 and computation signal S₂−S₃ is−54 mV under current I₁(LOAD1)=30 A and current I₂(LOAD2)=0 A in case ofNo. 5 and computation signal S₂−S₃ is −54 mV under current I₁(LOAD1)=30A and current I₂(LOAD2)=15 A in case of No. 11. Consequently, it wasconfirmed that the computation result was a signal of about three timescase of a hall device.

Further, when the disturbing magnetic field n existed, as shown in FIG.7, substantially the same result as when the disturbing magnetic fielddid not exist was obtained. As a result, the computation signal does notcontain an influence of the disturbing magnetic field n so that thedisturbing magnetic field n is canceled.

In case of No. 5, output signal S₁ from the first hall device 21 is −19mV under current I₁(LOAD1)=30 A and current I₁(LOAD2)=0 A. In case ofNo. 8, output signal S₃ from the third hall device 23 is 21 mV undercurrent I₂(LOAD2)=30 A and current I₁(LOAD1)=0 A. In case of No. 4,computation signal S₂−S₃ is −59 mV under current I₁(LOAD1)=30 A andcurrent I₂(LOAD2)=30 A. In case of No. 5, computation signal S₂−S₃ is−59 mV under current I₁(LOAD1)=30 A and current I₂(LOAD2)=0 A. In caseof No. 11, computation signal S₂−S₃ is −56 mV under current I₁(LOAD1)=30A and current I₂(LOAD2)=15 A. Consequently, it was confirmed that whenthe disturbing magnetic field n existed, the computation result was asignal of about three times case of a hall device.

As described above, in the current detecting apparatus according to thefirst embodiment, using three conductors disposed in Y shape and threehall devices, currents flowing through the respective conductors aredetected each by obtaining a difference of voltage between two halldevices which sandwich the conductor. Thus, as a current flowing througheach conductor, three times output can be obtained without beingaffected by the disturbing magnetic field, so that a highly accuratemeasurement of current is possible.

If as shown in FIG. 4, the current detecting apparatus of the firstembodiment is applied for a branch point to the battery, generator andload in automobile, this is available for charge/discharge control.

Further, because the current detecting apparatus according to the firstembodiment does not use the magnetic core, the weight and occupiedvolume can be reduced as compared to a case where the magnetic core isattached to each conductor thereby totally three magnetic cores beingattached, and further, production cost can be reduced largely. Further,frequency characteristic is improved and there is no magneticsaturation.

Second Embodiment

The second embodiment is an example in which n of the present inventionis “3” and m is “4”. FIG. 11 is a plan view showing a structure of thecurrent detecting apparatus according to the second embodiment of thepresent invention. This sensor portion is comprised of a conductor 10, afirst hall device 21, a second hall device 22, a third hall device 23and fourth hall device 24. Usually, these components are incorporated inan electric connecting box. In the second embodiment, no magnetismcollecting core is used.

As shown in FIG. 11, the conductor 10 is comprised of a first conductor11 having an end thereof at the branch point O contained in a flatplane, a second conductor 12 disposed at 90° in counterclockwisedirection from the first conductor 11 having an end at the branch pointO and a third conductor 13 disposed at 90° in counterclockwise directionfrom the second conductor 12 having an end at the branch point O. Thatis, the first conductor 11, second conductor 12 and third conductor 13are disposed in T shape on the flat plane including the branch point O.The first conductor 11, second conductor 12 and third conductor 13correspond to n conductors in the present invention. An end of each ofthese conductors is connected to the branch point O.

In the meantime, the conductor 10 may be composed by connecting ends ofthe three separate conductors, namely, the first conductor 11, secondconductor 12 and third conductor 13 at the branch point O and instead byforming integrally the first conductor 11, second conductor 12 and thirdconductor 13. Further, it is also permissible to compose this conductor10 by forming a wiring pattern having three branch routes including thefirst conductor 11, second conductor 12 and third conductor 13 on asubstrate.

A first hall device 21, second hall device 22, third hall device 23 andfourth hall device 24 correspond to m electromagnetic transducers of thepresent invention. Each hall device generates a voltage (hall voltage)signal corresponding to a density of magnetic flux entering itsmagnetism sensitive surface. A predetermined current is supplied to eachhall device through a lead (not shown) and the voltage signal generatedin each hall device is fetched out through a lead (not shown).

Positions where the respective hall devices are disposed are determinedas follows. That is, the first hall device 21 is disposed between thefirst conductor 11 and the second conductor 12 and at the same distancefrom these conductors. The second hall device 22 is disposed between thesecond conductor 12 and the third conductor 13 and at the same distancefrom these conductors. The third hall device 23 is disposed at aposition symmetrical to the second hall device 12 with respect to thethird conductor 13 as a symmetrical line. The fourth hall device 24 isdisposed at a position symmetrical to the first hall device 11 withrespect to the first conductor 11 as a symmetrical line. The respectivehall devices are disposed at the same distance from the branch point andnear the branch point. The magnetism sensitive surfaces of therespective hall devices substantially coincide with the flat planeincluding the branch point O and are disposed such that they aredirected in the same direction.

Next, an operation of the current detecting apparatus according to thesecond embodiment of the present invention having such a structure willbe described.

Assume that the magnetism sensitive surface of each hall device isdirected from a paper face toward yourself. Further assume that acurrent I₁ flows from the branch point O to its end in the firstconductor 11, a current I₂ flows from the end to the branch point O inthe second conductor 12 and a third current I₃ flows from the branchpoint O to the end in the third conductor I₃. The direction of currentflow mentioned here is just an example and it is not limited to theabove described one but any direction. Because the respective halldevices are disposed near each other and the magnetism sensitivesurfaces of the respective hall devices are directed to the samedirection, it is assumed that the respective magnetism sensitivesurfaces receive disturbing magnetic flux n equally.

If magnetic flux entering a magnetism sensitive surface of each of halldevices disposed on both sides of a conductor i when a current Ii flowsto the conductor i (i=1, 2, 3) is f(I_(i)) and magnetic flux going outof the magnetism sensitive surface is f(I_(i)), total magnetic flux B₁received by a magnetism sensitive plane of the first hall device 21 is“B₁=f(I₁)−f(I₂)+n”. Total magnetic flux B₂ received by the magnetismsensitive surface of the second hall device 22 is “B₂=f(I₂)−f(I₃)+n.Total magnetic flux received B₃ by the magnetism sensitive surface ofthe third hall device 23 is “B₃=f(I₃)+n. Total magnetic flux B₄ receivedby the magnetism sensitive surface of the fourth hall device 24 is“B₄=−f(I₁)+n”.

Now, if “B₂−B₁” is calculated, it comes that“B₂−B₁=f(I₂)−f(I₃)+n−{f(I₁)−f(I₂)+n}=2*f(I₂)−f(I₃)−f(I₁)”. Because“I₁+I₃=I₂”for the reason of Kirchhoff formula, “B₂−B₁=3*f(I₂)” isobtained.

Next, if “B₃−B₂” is calculated, it comes that“B₃−B₂=f(I₃)+n−{f(I₂)−f(I₃)+n}=2*f(I₃)−f(I₂)”. Because“f(I₁)+f(I₃)=−f(I₂)” is established for the reason of Kirchhoff formula,“B₃−B₂=3*f(I₃)+f(I₁)” is obtained.

Further, if “B₁−B₄” is calculated, it comes that“B₁−B₄=f(I₁)−f(I₂)+n−{−f(I₁)+n}=2*f(I₁)−f(I₂)”. Because“f(I₁)+f(I₃)=−f(I₂)” is established for the reason of Kirchhoff formula,“B₁−B₄=3*f(I₁)+f(I₃) is obtained.

Next, using the above described computation result, “3*(B₁−B₄)−(B₃−B₂)”is calculated,“3*(B₁−B₄)−(B₃−B₂)=3*{3*f(I₁)+f(I₃)}−{3*f(I₃)+f(I₁)}=8*f(I₁)” isobtained.

Further, if “3*(B₃−B₂)−(B₁−B₄)” is calculated,“3*(B₃−B₂)−(B₁−B₄)=3*{3*f(I₃)+f(I₁)}−{3*f(I₁)+f(I₃)}=8*f(I₃)” isobtained.

When the current I₂ flowing through the second conductor 12, currentI₁flowing through the first conductor 11 and current I₃ flowing throughthe third conductor are detected, results of computation of “B₂−B₁”,“3*(B₁−B₄)−(B₃−B₂)” and “3*(B₃−B₂)−(B₁−B₄)” becomes equal to generatingof a magnetic flux three times, eight times and eight times relative toa magnetic flux generated when a current flows through each conductor.Further, because the disturbing magnetic flux can be canceled, a currentcan be detected highly accurately. Further, because all the hall devicesare disposed near the branch point O, error factors such as temperaturedrift are canceled also.

FIG. 12 is a block diagram showing a structure of the operationprocessing circuit 30 of this current detecting apparatus. An output ofthis operation processing circuit 30 is supplied to the CPU 40, forexample.

The operation processing circuit 30 receives inputs of the voltagesignal VB₁ supplied from the first hall device 21 corresponding to themagnetic flux B₁, voltage signal VB₂ supplied from the second halldevice 22 corresponding to the magnetic flux B₂, voltage signal VB₃supplied from the third hall device 23 corresponding to the magneticflux B₃ and voltage signal VB₄ supplied from the fourth hall device 24corresponding to the magnetic flux B₄.

This operation processing circuit 30 is comprised of, for example, aplurality of operation amplifiers. Then, these operation amplifierscarry out computation similar to “3*(B₁−B₄)−(B₃−B₂)” and supply itscomputation result to the CPU 40 as a first detection signal DT₁indicating the magnitude of the current I₁. Because this first detectionsignal DT₁ is similar to a signal obtained by electromagneticallyconverting a magnetic flux 8*f(I₁) eight times relative to a magneticflux f(I₁) generated by only the current I₁ the current I₁ flowingthrough the first conductor 11 can be detected.

An operation amplifier contained in the operation processing circuit 30carries out computation corresponding to “B₂−B₁” and supplies itscomputation result to the CPU 40 as the second detection signal DT₂indicating the magnitude of the current I₂. Because this seconddetection signal DT₂ is similar to a signal obtained byelectrogmagnetically converting a magnetic flux 3*f(I₂) which is threetimes a magnetic flux f(I₂) generated by only the current I₂, thecurrent I₂ flowing through the second conductor 12 can be detected at ahigh sensitivity.

Further, the operation amplifier contained in the operation processingcircuit 30 carries out computation corresponding to “3*(B₃−B₂)−(B₁−B₄)”and supplies its computation result to the CPU 40 as the third detectionsignal DT₃ indicating the magnitude of the current I₃. Because thisthird detection signal DT₃ corresponds to a signal obtained byelectromagnetically converting a magnetic flux 8*f(I₃) which is eighttimes a magnetic flux f(I₃) generated by only the current I₃, thecurrent I₃ flowing through the third conductor 13 can be detected at ahigh sensitivity.

The CPU 40 receives the first detection signal DT₁, the second detectionsignal DT₂ and the third detection signal DT₃ from the operationprocessing circuit 30, and determines the magnitudes of currents flowingthrough the first conductor 11, second conductor 12 and third conductor13 and if necessary, drives a current circuit breaker or the like.

As described above, in the current detecting apparatus according to thesecond embodiment, using three conductors disposed in T shape and fourhall devices, currents flowing through the respective conductors aredetected each by obtaining a difference of voltage between two halldevices which sandwich the conductor. Thus, as a current flowing througheach conductor, eight times, three times and eight times outputs can beobtained without being affected by the disturbing magnetic field, sothat a highly accurate, high sensitivity measurement of current ispossible.

Further, because the current detecting apparatus according to the secondembodiment does not use the magnetic core, the weight and occupiedvolume can be reduced as compared to a case where the magnetic core isattached to each conductor thereby totally three magnetic cores beingattached, and further, production cost can be reduced largely. Further,frequency characteristic is improved and there is no magneticsaturation.

Third Embodiment

The third embodiment is an example in which n of the present inventionis “4” and m is “4”. FIG. 13 is a plan view showing a structure of asensor portion of the current detecting apparatus according to the thirdembodiment of the present invention. This sensor portion is comprised ofa conductor 10, a first hall device 21, a second hall device 22, a thirdhall device 23 and a fourth hall device 24. Usually, these componentsare incorporated in an electric connecting box. In the third embodiment,no magnetism collecting core is used.

The conductor 10 is comprised of the first conductor 11, secondconductor 12, third conductor 13 and fourth conductor 14 disposed infour directions from a branch point O on a flat plane containing thebranch point O, as shown in FIG. 13. That is, the first conductor 11,second conductor 12, third conductor 13 and fourth conductor 14 aredisposed in cross shape on the flat plane including the branch point O.The first conductor 11, second conductor 12, third conductor 13 andfourth conductor 14 correspond to n conductors of the present invention.Ends of the respective conductors are connected at the branch point O.

In the meantime, the conductor 10 may be composed by connecting ends ofthe four separate conductors, namely, the first conductor 11, secondconductor 12, third conductor 13 and fourth conductor 14 at the branchpoint O and instead by forming integrally the first conductor 11, secondconductor 12, third conductor 13 and fourth conductor 14. Further, it isalso permissible to compose this conductor 10 by forming a wiringpattern having four branch routes including the first conductor 11,second conductor 12, third conductor 13 and fourth conductor 14 on asubstrate.

A first hall device 21, second hall device 22, third hall device 23 andfourth hall device 24 correspond to m electromagnetic transducers of thepresent invention. Each hall device generates a voltage (hall voltage)signal corresponding to a density of magnetic flux entering itsmagnetism sensitive surface. A predetermined current is supplied to eachhall device through a lead (not shown) and the voltage signal generatedin each hall device is fetched out through a lead (not shown).

Positions where the respective hall devices are disposed are determinedas follows. That is, the first hall device 21 is disposed between thefirst conductor 11 and the second conductor 12 and at the same distancefrom these conductors. The second hall device 22 is disposed between thesecond conductor 12 and the third conductor 13 and at the same distancefrom these conductors. The third hall device 23 is disposed between thethird conductor 13 and the fourth conductor 14 and at the same distancefrom these conductors. The fourth hall device 24 is disposed between thefourth conductor 14 and the first conductor 11 and at the same distancefrom these conductors. The respective hall devices are disposed at thesame distance from the branch point and near the branch point. Themagnetism sensitive surfaces of the respective hall devicessubstantially coincide with the plane including the branch point O andare disposed such that they are directed in the same direction.

Next, an operation of the current detecting apparatus according to thethird embodiment of the present invention having such a structure willbe described.

Assume that the magnetism sensitive surface of each hall device isdirected from a paper face toward yourself. Further assume that acurrent I₁ flows from the branch point O to its end in the firstconductor 11, a current I₂ flows from the end to the branch point O inthe second conductor 12, and a third current I₃ flows from the branchpoint O to the end in the third conductor I₃. The direction of currentflows mentioned here is just an example and it is not limited to theabove described one but any direction. Because the respective halldevices are disposed near each other and the magnetism sensitivesurfaces of the respective hall devices are directed to the samedirection, it is assumed that the respective magnetism sensitivesurfaces receive disturbing magnetic flux n equally.

If magnetic flux entering a magnetism sensitive surface of each of halldevices disposed on both sides of a conductor i when a current I_(i)flows to the conductor i (i=1, 2, 3, 4) is f(I_(i)) and magnetic fluxgoing out of the magnetism sensitive surface is −f(I_(i)), totalmagnetic flux B₁ received by a magnetism sensitive plane of the firsthall device 21 is “B₁=f(I₁)−f(I₂)+n”. Total magnetic flux B₂ received bythe magnetism sensitive surface of the second hall device 22 is“B₂=f(I₂)−f(I₃)+n”. Total magnetic flux received B₃ by the magnetismsensitive surface of the third hall device 23 is “B₃=f(I₃)−f(I₄)+n”.Total magnetic flux B₄ received by the magnetism sensitive surface ofthe fourth hall device 24 is “B₄=f(I₄)−f(I₁)+n”.

Now, if “B₂−B₁” is calculated, it comes that“B₂−B₁=f(I₂)−f(I₃)+n−{f(I₁)−f(I₂)+n}=2*f(I₂)−f(I₃)−f(I₁)”. Because“I₁+13=−(I₂+I₄)” for the reason of Kirchhoff formula,“f(I₁)+f(I₃)=−{f(I₂)+f(I₄)}” is established, “B₂−B₁=3*f(I₂)+f(I₄) isobtained.

Next, if “B₃−B₂” is calculated, it comes that“B₃−B₂=f(I₃)−f(I₄)+n−{f(I₂)−f(I₃)+n}=2*f(I₃)−f(I₄)−f(I₂)”. Because“f(I₁)+f(I₃)=−{f(I₂)+f(I₄)}” is established for the reason of Kirchhoffformula, “B₃−B₂=3*f(I₃)+f(I₁)” is obtained.

Next, if “B₄−B₃” is calculated, it comes that“B₄−B₃=f(I₄)−f(I₁)+n−{f(I₃)−f(I₄)+n}=2 *f(I₄)−f(I₁)−f(I₃)”. Because“f(I₁)+f(I₃)=−{f(I₂)+f(I₄)}” is established for the reason of Kirchhoffformula, “B₄−B₃=3*f(I₄)+f(I₂)” is obtained.

Further, if “B₁−B₄” is calculated, it comes that“B₁−B₄=f(I₁)−f(I₂)+n−{f(I₄)−f(I₁)+n}=2*f(I₁)−f(I₂)−f(I₄)”. Because“f(I₁)+f(I₃)=−{f(I₂)+f(I₄)}” is established for the reason of Kirchhoffformula, “B₁−B₄=3*f(I₁)+f(I₃)” is obtained.

Next, using the above described computation result, “3*(B₁−B₄)−(B₃−B₂)”is calculated,“3*(B₁−B₄)−(B₃−B₂)=3*{3*f(I₁)+f(I₃)}−{3*f(I₃)+f(I₁)}=8*f(I₁)” isobtained. Further, if “3*(B₂−B₁)−(B₄−B₃)” is calculated,“3*(B₂−B₁)−(B₄−B₃)=3*{3**f(I₂)+f(I₄)}−{3*f(I₄)+f(I₂)}=8*f(I₂)” isobtained.

Further, if “3*(B₃−B₂)−(B₁−B₄) is calculated,“3*(B₃−B₂)−(B₁−B₄)=3*{3*f(I₃)+f(I₁)}−{3*f(I₁)+f(I₃)}=8*f(I₃)” isobtained.

Further, if “3*(B₄−B₃)−(B₂−B₁) is calculated,“3*(B₄−B₃)−(B₂−B₁)=3*{3*f(I₄)+f(I₂)}−{3*f(I₂)+f(I₄)}=8*f(I₄)” isobtained.

When current I₁ flowing through the first conductor 11, the current I₂flowing through the second conductor 12, current I₃ flowing through thethird conductor 13 and current I₄ flowing through the fourth conductor14 are detected, results of computation of “3*(B₁−B₄)−(B₃−B₂)”,“3*(B₂−B₁)−(B₄−B₃)”, “3*(B₃−B₂)−(B₁−B₄)”, and “3*(B₄−B₃)−(B₂−B₁)”becomes equal to generating of a magnetic flux eight times a magneticflux generated when a current flows through each conductor. Further,because the disturbing magnetic flux can be canceled, a current can bedetected highly accurately. Further, because all the hall devices aredisposed near the branch point O, error factors such as temperaturedrift are canceled also.

FIG. 14 is a block diagram showing a structure of the operationprocessing circuit 30 of this current detecting apparatus. An output ofthis operation processing circuit 30 is supplied to the CPU 40, forexample. The operation processing circuit 30 receives inputs of thevoltage signal VB₁supplied from the first hall device 21 correspondingto the magnetic flux B₁, voltage signal VB₂ supplied from the secondhall device 22 corresponding to the magnetic flux B₂, voltage signal VB₃supplied from the third hall device 23 corresponding to the magneticflux B₃ and voltage signal VB₄ supplied from the fourth hall device 24corresponding to the magnetic flux B₄.

This operation processing circuit 30 is comprised of, for example, aplurality of operation amplifiers. Then, these operation amplifierscarry out computation similar to “3*(B₁−B₄)−(B₃−B₂)” and supply itscomputation result to the CPU 40 as a first detection signal DT₁indicating the magnitude of the current I₁. Because this first detectionsignal DT₁ is similar to a signal obtained by electromagneticallyconverting a magnetic flux 8*f(I₁) eight times a magnetic flux f(I₁)generated by only the current I₁, the current I₁ flowing through thefirst conductor 11 can be detected.

An operation amplifier contained in the operation processing circuit 30carries out computation corresponding to “3*(B₂−B₁)−(B₄−B₃)” andsupplies its computation result to the CPU 40 as the second detectionsignal DT₂ indicating the magnitude of the current I₂. Because thissecond detection signal DT₂ is similar to a signal obtained byelectrogmagnetically converting a magnetic flux 8*f(I₂) eight times amagnetic flux f(I₂) generated by only the current I₂, the current I₂flowing through the second conductor 12 can be detected at a highsensitivity.

An operation amplifier contained in the operation processing circuit 30carries out computation corresponding to “3*(B₃−B₂)−(B₁−B₄)” andsupplies its computation result to the CPU 40 as the third detectionsignal DT₃ indicating the magnitude of the current I₃. Because thisthird detection signal DT₃ is similar to a signal obtained byelectrogmagnetically converting a magnetic flux 8*f(I₃) eight times amagnetic flux f(I₃) generated by only the current I₃, the current I₃flowing through the second conductor 13 can be detected at a highsensitivity.

An operation amplifier contained in the operation processing circuit 30carries out computation corresponding to “3*(B₄−B₃)−(B₂−B₁)” andsupplies its computation result to the CPU 40 as the fourth detectionsignal DT₄ indicating the magnitude of the current I₄. Because thisfourth detection signal DT₄ is similar to a signal obtained byelectrogmagnetically converting a magnetic flux 8*f(I₄) eight times amagnetic flux f(I₄) generated by only the current I₄, the current I₄flowing through the second conductor 14 can be detected at a highsensitivity.

The CPU 40 receives the first detection signal DT₁, the second detectionsignal DT₂, the third detection signal DT₃ and the fourth detectionsignal DT₄ from the operation processing circuit 30, and determines themagnitudes of currents flowing through the first conductor 11, secondconductor 12, third conductor 13 and fourth conductor 14 and ifnecessary, drives a current circuit breaker or the like.

As described above, in the current detecting apparatus according to thethird embodiment, using four conductors disposed in cross shape and fourhall devices, currents flowing through the respective conductors aredetected each by obtaining a difference of voltage between two halldevices which sandwich the conductor. Thus, as a current flowing througheach conductor, eight times outputs can be obtained without beingaffected by the disturbing magnetic field, so that a highly accuratemeasurement of current is possible.

Further, because the current detecting apparatus according to the thirdembodiment does not use the magnetic core, the weight and occupiedvolume can be reduced as compared to a case where the magnetic core isattached to each conductor thereby totally four magnetic cores beingattached, and further, production cost can be reduced largely. Further,frequency characteristic is improved and there is no magneticsaturation.

Fourth Embodiment

The fourth embodiment is an example in which n of the present inventionis “3” and m is “3”. FIG. 15 is a perspective view showing a structureof the current detecting apparatus according to the fourth embodiment ofthe present invention. This sensor portion is comprised of a conductor10, a first hall device 21, a second hall device 22 and a third halldevice 23. Usually, these components are incorporated in an electricconnecting box. In the first embodiment, no magnetism collecting core isused.

As shown in FIG. 15, the conductor 10 is comprised of a first conductor11, second, conductor 12 and third conductor 13 disposed radially onthree-dimensional axes perpendicular to each other with the branch pointO as a home position. That is, the first conductor 11 is disposed in theX-axis direction, the second conductor 12 is disposed in the y-axisdirection and the third conductor 13 is disposed in the z-axisdirection. The first conductor 11, second conductor 12 and thirdconductor 13 correspond to n conductors of the present invention. An endof each of the conductors is connected to the branch point O. The otherend of each of the conductors is connected to a power supply or a load45.

In the meantime, the conductor 10 may be composed by connecting ends ofthe three separate conductors, namely, the first conductor 11, secondconductor 12 and third conductor 13 at the branch point O and instead byforming integrally the first conductor 11, second conductor 12 and thirdconductor 13. Further, it is also permissible to compose this conductor10 by forming a wiring pattern having three branch routes including thefirst conductor 11, second conductor 12 and third conductor 13 on asubstrate.

The first hall device 21, second hall device 22 and third hall device 23correspond to m electromagnetic transducers of the present invention.The respective hall devices are disposed on a plane formed by the firstconductor 11 and the second conductor 12, that is, x-y plane. Therespective hall devices generate a voltage (hall voltage) correspondingto magnetic density entering its magnetism sensitive surface (magneticflux detecting plane). A predetermined current is supplied to each halldevice through a lead (not shown) and a voltage signal generated in eachhall device is fetched out through a lead (not shown).

Positions where the respective hall devices are disposed are determinedas follows. That is, the first hall device 21 is disposed between thefirst conductor 11 and the second conductor 12 and at the same distancefrom these conductors. The second hall device 22 is disposedsymmetrically with the first hall device 21 with respect to the secondconductor 12. The third hall device 23 is disposed symmetrically withthe first hall device 21 with respect to the first conductor 11. Therespective hall devices are disposed at the same distance from thebranch point O and near the branch point. The magnetism sensitivesurfaces of the respective hall devices substantially coincide with thex-y plane and are disposed such that they are directed in the samedirection.

Next, an operation of the sensor portion of the current detectingapparatus according to the fourth embodiment of the present inventionhaving such a structure will be described.

Assume that the magnetism sensitive surface of each hall device isdirected in the z-axis direction. Further assume that a current I₁ flowsfrom its end to the branch point O in the first conductor 11, a currentI₂ flows from its end to the branch point O in the second conductor 12and a third current I₃ flows from its end to the branch point O in thethird conductor I₃. The direction of current flow mentioned here is justan example and it is not limited to the above described one but anydirection. Because the respective hall devices are disposed near eachother and the magnetism sensitive surfaces of the respective halldevices are directed to the same direction, it is assumed that therespective magnetism sensitive surfaces receive disturbing magnetic flux−nz in the z-axis direction equally.

If magnetic flux entering a magnetism sensitive surface of each of halldevices disposed on both sides of a conductor i when a current I_(i)flows to the conductor i (i=1, 2, 3) is f(I_(i)) and magnetic flux goingout of the magnetism sensitive surface is −f(I_(i)), total magnetic fluxB₁ received by a magnetism sensitive surface of the first hall device 21is “B₁=f(I₁)−f(I₂)−nz”. Total magnetic flux B₂ received by the magnetismsensitive surface of the second hall device 22 is “B₂=f(I₂)−nz”. Totalmagnetic flux B₃ received by the magnetism sensitive surface of thethird hall device 23 is “B₃=−f(I₁)−nz”.

Now, if “B₂−B₃” is calculated, it comes that“B₂−B₃=f(I₂)−nz−{−f(I₁)−nz}=f(I₁)+f(I₂)”. Because “f(I₁)+f(I₂)=−f(I₃)”is established for the reason of Kirchhoff formula, “B₂−B₃=−f(I₃)” isobtained.

Further, if “B₁+B₂” is calculated, it comes that“B₁+B₂=f(I₁)−f(I₂)−nz+{f(I₂)−nz}=f(I₁)−2*nz”. Further, if “B₁+B₂−2*B₃”is calculated, it comes that“B₁+B₂−2*B₃=f(I₁)−2*nz−2*{−f(I₁)−nz}=3*f(I₁)”.

Further, if “B₁+B₃” is calculated, it comes that“B₁+B₃=f(I₁)−f(I₂)−nz+{−f(I₁)−nz}=−f(I₂)−2*nz”. Further, if “B₁+B₃−2*B₂”is calculated, it comes that“B₁+B₃−2*B₂=−f(I₂)−2*nz−2*{f(I₂)−nz}=−3*f(I₂)”.

That is, by calculating “B₁+B₂−2*B₃” and “B₁+B₃−2*B₂”, its resultbecomes equal to obtaining of a magnetic flux three times a magneticflux generated when the current I₁ flows through the first conductor 11or obtaining of a magnetic flux three times a magnetic flux generatedwhen the current I₂ flows through the second conductor 12. Consequently,the first conductor 11 and the second conductor 12 existing on the sameplane as the hall devices are capable of securing an output three timesa current flowing through the first conductor 11 and the secondconductor 12 respectively.

Because the disturbing magnetic flux nz can be canceled by carrying outthe above described operation, the current can be detected veryaccurately. Because all the hall devices are disposed near the branchpoint O, error factors such as temperature drift are canceled also.

Because the magnetic core is not used, the weight and occupied volumecan be reduced as compared to a case where a magnetic core is attachedto each conductor thereby totally three cores being attached and theproduction cost can be reduced largely. Further, the frequencycharacteristic is improved and there is no magnetic saturation.

FIG. 16 is a block diagram showing the structure of the currentdetecting apparatus containing the above described sensor portion. Inthis current detecting apparatus, the sensor portion is comprised of theconductor 10, first hall device 21, second hall device 22 and third halldevice 23 and further, an operation processing circuit 30 is addedthereto. An output from the operation processing circuit 30 is suppliedto, for example, the CPU 40.

The operation processing circuit 30 receives inputs of the voltagesignal VB₁ from the first hall device 21 corresponding to the magneticflux B₁, voltage signal VB₂ from the second hall device 22 correspondingto the magnetic flux B₂ and voltage signal VB₃ from the third halldevice 23 corresponding to the magnetic flux B₃.

This operation processing circuit 30 is comprised of, for example, aplurality of operation amplifiers. Then, these operation amplifierscarry out computation similar to “B₁+B₂−2*B₃” and supply its computationresult to the CPU 40 as a first detection signal DT₁ indicating themagnitude of the current I₁. Because this first detection signal DT₁ issimilar to a signal obtained by electromagnetically converting amagnetic flux 3*f(I₁) three times a magnetic flux f(I₁) generated byonly the current I₁, the current I₁ flowing through the first conductor11 can be detected.

An operation amplifier contained in the operation processing circuit 30carries out computation corresponding to “B₁+B₃−2*B₂” and supplies itscomputation result to the CPU 40 as the second detection signal DT₂indicating the magnitude of the current I₂. Because this seconddetection signal DT₂ is similar to a signal obtained byelectrogmagnetically converting a magnetic flux 3 *f(I₂) three times amagnetic flux f(I₂) generated by only the current I₂, the current I₂flowing through the second conductor 12 can be detected at a highsensitivity.

Further, the operation amplifier contained in the operation processingcircuit 30 carries out computation corresponding to “B₂−B₃” and suppliesits computation result to the CPU 40 as the third detection signal DT₃indicating the magnitude of the current I₃. Because this third detectionsignal DT₃ corresponds to a signal obtained by electromagneticallyconverting a magnetic flux f(I₃) generated by only the current I₃, thecurrent I₃ flowing through the third conductor 13 can be detected at ahigh sensitivity.

The CPU 40 receives the first detection signal DT₁, the second detectionsignal DT₂ and the third detection signal DT₃ from the operationprocessing circuit 30, and determines the magnitudes of currents flowingthrough the first conductor 11, second conductor 12 and third conductor13 and if necessary, drives a current circuit breaker or the like.

According to the current detecting apparatus of the fourth embodiment,three conductors disposed on the respective axes of three-dimensionalaxes and three hall devices are used. A current flowing through eachconductor is detected by obtaining a difference between voltage signalsfrom two hall devices which sandwich the first conductor and the secondconductor on the xy plane. Three times, three times and one time outputscan be obtained as currents flowing through the first conductor, secondconductor and third conductor respectively without being affected bydisturbing magnetic field, thereby achieving a highly accuratemeasurement of current.

Further, because the current detecting apparatus according to the fourthembodiment does not use the magnetic core, the weight and occupiedvolume can be reduced as compared to a case where the magnetic core isattached to each conductor thereby totally three magnetic cores beingattached, and further, production cost can be reduced largely. Further,frequency characteristic is improved and there is no magneticsaturation.

Fifth Embodiment

The fifth embodiment is an example in which n of the present inventionis “4” and m is “4”. FIG. 17 is a perspective view showing a structureof a sensor portion of the current detecting apparatus according to thefifth embodiment of the present invention. This sensor portion iscomprised of a conductor 10, a first hall device 21, a second halldevice 22, a third hall device 23 and a fourth hall device 24. Usually,these components are incorporated in an electric connecting box. In thefifth embodiment, no magnetism collecting core is used.

As shown in FIG. 17, the conductor 10 is comprised of a first conductor11, second conductor 13, third conductor 13 and fourth conductor 14disposed radially on three-dimensional axes each perpendicular to otheraxes with the branch point O as a home position. That is, the firstconductor 11 is disposed in the x-axis direction, the second conductor12 is disposed in the y-axis direction, the third conductor 13 isdisposed in the x-axis direction and the fourth conductor is disposed inthe z-axis direction. The first conductor 11, second conductor 12, thirdconductor 13 and fourth conductor 14 correspond to n conductors of thepresent invention. An end of each conductor is connected to the branchpoint O and the other end thereof is connected to a power supply or load45.

In the meantime, the conductor 10 may be composed by connecting ends ofthe four separate conductors, namely, the first conductor 11, secondconductor 12, third conductor 13 and fourth conductor 14 at the branchpoint O and instead by forming integrally the first conductor 11, secondconductor 12, third conductor 13 and fourth conductor 14. Further, it isalso permissible to compose this conductor 10 by forming a wiringpattern having four branch routes including the first conductor 11,second conductor 12, third conductor 13 and fourth conductor 14 on asubstrate.

A first hall device 21, second hall device 22, third hall device 23 andfourth hall device 24 correspond to m electromagnetic transducers of thepresent invention. The respective hall devices are disposed on a planeformed by the first conductor 11, second conductor 12 and thirdconductor 13, that is, the xy plane. Each hall device generates avoltage (hall voltage) signal corresponding to a density of magneticflux entering its magnetism sensitive surface. A predetermined currentis supplied to each hall device through a lead (not shown) and thevoltage signal generated in each hall device is fetched out through alead (not shown).

Positions where the respective hall devices are disposed are determinedas follows. The first hall device 21 and second hall device 22 aredisposed at positions at the same distance from the first conductor 11of the first conductor 11-third conductor 13 which exist on the xyplane. The third hall device 23 is disposed symmetrically with thesecond hall device 22 with respect to the second conductor 12 as asymmetrical line. The fourth hall device 24 is disposed symmetricallywith the third hall device 23 with respect to the third conductor 13 asa symmetrical line. The respective hall devices are disposed at the samedistance from the branch point O and near the branch point O. Further,the magnetism sensitive surfaces of the respective hall devices aredisposed such that they substantially coincide with the xy plane and aredirected in the same direction.

Next, an operation of the sensor portion of the current detectingapparatus according to the fifth embodiment of the present inventionhaving such a structure will be described below.

Assume that the magnetism sensitive surface of each hall device isdirected in the z-axis direction. Further assume that a current I₁ flowsfrom an end of the first conductor 11 to the branch point O, a currentI₂ flows from the end of the second conductor 12 to the branch point O,a current I₃ flows from the end of the third conductor 13 to the branchpoint O and a current I₄ flows from the end of the fourth conductor 14to the branch point O. The direction of current flows mentioned here isjust an example and it is not limited to the above described one but anydirection. Because the respective hall devices are disposed near eachother and the magnetism sensitive surfaces of the respective halldevices are directed in the same direction, it is assumed that therespective magnetism sensitive surfaces receive z-axis directioncomponent −nz of the disturbing magnetic flux equally.

If magnetic flux entering a magnetism sensitive surface of each of halldevices disposed on both sides of a conductor i when a current I_(i)flows to the conductor i (i=1, 2, 3) is f(I_(i)) and magnetic flux goingout of the magnetism sensitive surface is −f(I_(i)), total magnetic fluxB₁ received by a magnetism sensitive surface of the first hall device 21is “B₁=−f(I₁)−nz”. Total magnetic flux B₂ received by the magnetismsensitive surface of the second hall device 22 is “B₂=f(I₁)−f(I₂)−nz”.Total magnetic flux received B₃ by the magnetism sensitive surface ofthe third hall device 23 is “B₃=f(I₂)−f(I₃)−nz”. Total magnetic flux B₄received by the magnetism sensitive surface of the fourth hall device 24is “B₄=f(I₃)−nz”.

Now, if “B₁+B₂” is calculated,“B₁+B₂=−f(I₁)−nz+{f(I₁)−f(I₂)−nz}=−f(I₂)−2*nz” is obtained. If “B₃+B₄”is calculated, “B₃+B₄=f(I₂)−f(I₃)−nz+{f(I₃)−nz}=f(I₂)−2*nz” is obtained.Further, if “B₁+B₂−B₃−B₄” is calculated,“B₁+B₂−B₃−B₄=−f(I₂)−2*nz−f(I₂)+2*nz=−2*f(I₂)” is obtained.

If “B₂+B₃+B₄” is calculated,“B₂+B₃+B₄=f(I₁)−f(I₂)−nz+f(I₂)−f(I₃)−nz+f(I₃)−nz=f(I₁)−3*nz” isobtained. Further, if “B₂+B₃+B₄−3*B₁” is calculated,“B₂+B₃+B₄−3*B₁=f(I₁)−3*nz−3*{−f(I₁)−nz}=4*f(I₁) is obtained.

Next, if “−B−B₂−B₃” is calculated,“−B₁−B₂−B₃=f(I₁)+nz−f(I₁)+f(I₂)+nz−f(I₂)+f(I₃)+nz=f(I₃)+3*nz” isobtained. If “−B₁−B₂−B₃+3*B₄” is calculated,“−B₁−B₂−B₃+3*B₄=f(I₃)+3*nz+3*{f(I₃)−nz}=4*f(I₃)” is obtained.

Next, if “2*B₂−2*B₃” is calculated,“2*B₂−2*B₃=2*{f(I₁)−f(I₂)−nz}−2*{f(I₂)−f(I₃)−nz}=2*f(I₁)−2*f(I₂)+2*f(I₃)”is obtained. If “2*B₂−2*B₃+6*B₁−6*B₄” is calculated,“2*B₂−2*B₃+6*B₁−6*B₄”=2*f(I₁)−4*f(I₂)+2*f(I₃)+6*−{f(I₃)−nz}−6*{f(I₃)−nz}=−4*{f(I₁)+f(I₂)+f(I₃)}”is obtained. Here, because “f(I₁)+f(I₂)+f(I₃)=−f(I₄)” is establishedbecause of Kirchhoff formula, “2*B₂−2*B₃+6*B₁−6*B₄=4*f(I₄)” is obtained.

That is, by calculating “B₂+B₃+B₄−3*B₁”, a result of the calculationbecomes equal to obtaining of a magnetic flux four times a magnetic fluxgenerated when the current I₁ flows through the first conductor 11. Bycalculating “−B₁−B₂−B₃+3*B₄”, a result of calculation becomes equal toobtaining of a magnetic flux four times a magnetic flux generated whenthe current I₃ flows through the third conductor 13. Further, bycalculating “2*B₂−2*B₃+6*B₁−6*B₄”, a result of calculation becomes equalto obtaining of a magnetic flux four times a magnetic flux generatedwhen the current I₄ flows through the fourth conductor 14. Then, bycalculating “B₁+B₂−B₃−B₄”, a result of calculation becomes equal toobtaining of a magnetic flux two times a magnetic flux generated whenthe current I₂ flows through the second conductor 12.

Further, by the above described operation, the disturbing magnetic fluxnz can be canceled, so that a highly accurate current detection ispossible. Additionally, because all the hall devices are disposed nearthe branch point O, error factors such as temperature drift are canceledin the same way.

Further, because the current detecting apparatus according to the fifthembodiment does not use the magnetic core, the weight and occupiedvolume can be reduced as compared to a case where the magnetic core isattached to each conductor thereby totally four magnetic cores beingattached, and further, production cost can be reduced largely. Further,frequency characteristic is improved and there is no magneticsaturation.

FIG. 18 is a block diagram showing a structure of the current detectingapparatus containing the sensor portion. This current detectingapparatus is composed by adding an operation processing circuit 30 tothe sensor portion comprised of the conductor 10, first hall device 21,second hall device 22, third hall device 23 and fourth hall device 24.An output of this operation processing circuit 30 is supplied to the CPU40, for example.

The operation processing circuit 30 receives inputs of the voltagesignal VB corresponding to the magnetic flux B₁ from the first halldevice 21, voltage signal VB₂ corresponding to the magnetic flux B₂ fromthe second hall device 22, voltage signal VB₃ corresponding to themagnetic flux B₃ from the third hall device 23 and voltage signal VB₄corresponding to the magnetic flux B₄ from the fourth hall device 24.

This operation processing circuit 30 can be comprised of a plurality ofoperation amplifiers. Then, these operation amplifiers carry outoperation corresponding to “B₂+B₃+B₄−3*B¹”. Its operation result issupplied to the CPU 40 as a first detection signal DT₁ indicating themagnitude of the current I₁. Because this first detection signal DT₁ issimilar to a signal obtained by electromagnetically converting amagnetic flux 4*f(I₁) four times a magnetic flux f(I₁) generated by onlythe current I₁, the current I₁ flowing through the first conductor 11can be detected with a high sensitivity.

Further, the operation amplifier contained in the operation processingcircuit 30 carries out operation corresponding to “B₁+B₂−B₃−B₄” andsupplies its operation result to the CPU 40 as a second detection signalDT₂ indicating the magnitude of the current I₂. Because this seconddetection signal DT₂ is similar to a signal obtained byelectromagnetically converting a magnetic flux 2*f(I₂) twice a magneticflux f(I₂) generated by only the current I₂, the current I₂ flowingthrough the second conductor 12 can be detected with a high sensitivity.

Further, the operation amplifier contained in the operation processingcircuit 30 carries out operation corresponding to and supplies itsoperation result to the CPU 40 as a third detection signal DT₃indicating the magnitude of the current I₃. Because this third detectionsignal DT₃ is similar to a signal obtained by electromagneticallyconverting a magnetic flux 4*f(I₃) which is four times a magnetic fluxf(I₃) generated by only the current I₃, the current I₃ flowing throughthe second conductor 13 can be detected with a high sensitivity.

Further, the operation amplifier contained in the operation processingcircuit 30 carries out operation corresponding to “2*B₂−2*B₃+6*B₁−6* B₄”and supplies its operation result to the CPU 40 as a fourth detectionsignal DT₄ indicating the magnitude of the current I₄. Because thisfourth detection signal DT₄ is similar to a signal obtained byelectromagnetically converting a magnetic flux 4*f(I₄) which is fourtimes a magnetic flux f(I₄) generated by only the current I₄, thecurrent I4 flowing through the second conductor 14 can be detected witha high sensitivity.

The CPU 40 receives inputs of the first detection signal DT₁ from theoperation processing circuit 30, second detection signal DT₂, thirddetection signal DT₃ and fourth detection signal DT₄. Then it judges themagnitude of current flowing through each of the first conductor 11,second conductor 12, third conductor 13 and fourth conductor 14, andthen drives the current circuit breaker or the like as required.

According to the current detecting apparatus of the fifth embodiment,four conductors disposed on the respective axes of three-dimensionalaxes and −x axis and four hall devices are used. A current flowingthrough each conductor is detected by obtaining a difference betweenvoltage signals from two hall devices which sandwich each of the firstconductor-third conductor on the xy plane without being affected bydisturbing magnetic field. Further, outputs four times, two times, fourtimes and four times can be obtained as the current flowing through thefirst conductor-fourth conductor, respectively. As a result, a highlyaccurate current measurement is enabled and the disturbing magnetic fluxexisting near the current detecting apparatus is canceled.

Because the current detecting apparatus according to the fifthembodiment does not use the magnetic core, the weight and occupiedvolume can be reduced as compared to a case where the magnetic core isattached to each conductor thereby totally four magnetic cores beingattached, and further, production cost can be reduced largely. Further,frequency characteristic is improved and there is no magneticsaturation.

Sixth Embodiment

The sixth embodiment has a feature that it is capable of obtaining acurrent at a better accuracy than the current detecting apparatus of thesecond embodiment. Because the current detecting apparatus of the sixthembodiment is of the same structure as the current detecting apparatusof the second embodiment shown in FIGS. 11, 12, an operation thereofwill be described.

First, an equation shown in Expression 1 is established about variables,currents I_(i)-I₃ and magnetic fluxes B₁-B₄ because of Biot-Savart'slaw. $\begin{matrix}{{B_{1} = {{\frac{1}{4\quad \pi \quad r}\left\lbrack {{{- \left( {1 + \frac{1}{\sqrt{2}}} \right)}I_{1}} + {\left( {1 + \frac{1}{\sqrt{2}}} \right)I_{2}} + {\left( {1 - \frac{1}{\sqrt{2}}} \right)I_{3}}} \right\rbrack}\quad (1)}}{B_{2} = {{{{\frac{1}{4\pi \quad r}\left\lbrack {{{- \left( {1 - \frac{1}{\sqrt{2}}} \right)}I_{1}} - {\left( {1 + \frac{1}{\sqrt{2}}} \right)I_{2}} + {\left( {1 + \frac{1}{\sqrt{2}}} \right)I_{3}}} \right\rbrack}\quad (2)B_{3}} = {{{{\frac{1}{4\pi \quad r}\left\lbrack {{\left( {1 - \frac{1}{\sqrt{2}}} \right)I_{1}} - {\left( {1 - \frac{1}{\sqrt{2}}} \right)I_{2}} - {\left( {1 + \frac{1}{\sqrt{2}}} \right)I_{3}}} \right\rbrack}\quad (3)B_{4}} = {{{{\frac{1}{4\pi \quad r}\left\lbrack {{\left( {1 + \frac{1}{\sqrt{2}}} \right)I_{1}} + {\left( {1 - \frac{1}{\sqrt{2}}} \right)I_{2}} - {\left( {1 - \frac{1}{\sqrt{2}}} \right)I_{3}}} \right\rbrack}\quad (4)0} = {I_{1} + I_{2} + {I_{3}\quad (5)}}}}}}}}}} & \left\lbrack {{Expression}\quad 1} \right\rbrack\end{matrix}$

If equation (1) is subtracted from equation (2) in Expression 1,Expression 2 is obtained. [Expression 2]

4{square root over (2)}πr(B ₂ −B ₁)=2I ₁−2({square root over (2)}+1)I₂+2I ₃  (6)

Further, Expression 3 is obtained from equation (5) of Expression 1 andcurrent I₂ is obtained from this Expression 3. $\begin{matrix}{I_{2} = {{{- \frac{2\sqrt{2}}{\sqrt{2} + 2}} \cdot \pi}\quad {r\left( {B_{2} - B_{1}} \right)}\quad (7)}} & \left\lbrack {{Expression}\quad 3} \right\rbrack\end{matrix}$

If equation (1) is subtracted from equation (4) of Expression 1,Expression 4 is obtained.

[Expression 4]

4{square root over (2)}πr(B ₄ −B ₁)=2({square root over (2)}+1)I ₁−2I₂−2({square root over (2)}−1)I ₃  (8)

If equation (2) is subtracted from equation (3) of Expression 1,Expression 5 is obtained.

[Expression 5]

4{square root over (2)}πr(B ₃ −B ₂)=2({square root over (2)}−1)I ₁30 2I₂−2({square root over (2)}+1)I ₃  (9)

If equation (8) is added to equation (9), Expression 6 is obtained.

[Expression 6]

4{square root over (2)}πr(−B ₁ −B ₂ +B ₃ +B ₄)=4{square root over (2)}I₁−4{square root over (2)}I ₃  (10)

If equation (5) is substituted into equation (10), Expression 7 isobtained.

[Expression 7]

4{square root over (2)}πr(−B ₁ −B ₂ +B ₃ +B ₄)=8{square root over (2)}I₁+4{square root over (2)}I ₂  (11)

Further, Expression 8 is obtained from equation (7). $\begin{matrix}{{{8\sqrt{2}I_{1}} = {{4\sqrt{2}\pi \quad {r\left( {{- B_{1}} - B_{2} + B_{3} + B_{4}} \right)}} - {{\frac{4{\sqrt{2} \cdot 2}\sqrt{2}}{\sqrt{2} + 2} \cdot \pi}\quad {r\left( {B_{2} - B_{1}} \right)}\quad (12)}}}{I_{1} = {{\frac{1}{2}\quad \pi \quad {r\left( {{- B_{1}} - B_{2} + B_{3} + B_{4}} \right)}} - {2\left( {\sqrt{2} - 1} \right)\pi \quad {r\left( {B_{2} - B_{1}} \right)}\quad (13)}}}} & \left\lbrack {{Expression}\quad 8} \right\rbrack\end{matrix}$

Current I₁ is obtained from equation (13). For I₃, if equation (5) issubstituted into equation (10), Expression 9 is obtained.

[Expression 9]

4{square root over (2)}πr(−B ₁ −B ₂ +B ₃ +B ₄)=−4{square root over (2)}I₂−8{square root over (2)}I ₃  (14)

Further, Expression 10 is obtained from equation (7). $\begin{matrix}{{{8\sqrt{2}I_{3}} = {{4\sqrt{2}\pi \quad {r\left( {{- B_{1}} - B_{2} + B_{3} + B_{4}} \right)}} + {{\frac{4{\sqrt{2} \cdot 2}\sqrt{2}}{\sqrt{2} + 2} \cdot \pi}\quad {r\left( {B_{2} - B_{1}} \right)}\quad (15)}}}{I_{3} = {{\frac{1}{2}\quad \pi \quad {r\left( {{- B_{1}} - B_{2} + B_{3} + B_{4}} \right)}} + {2\left( {\sqrt{2} - 1} \right)\pi \quad {r\left( {B_{2} - B_{1}} \right)}\quad (16)}}}} & \left\lbrack {{Expression}\quad 10} \right\rbrack\end{matrix}$

I₁ will be obtained from the equation (16). In this way, each of I₁, I₂,I₃ can be calculated by multiplying a difference between magnetic fieldsreceived by two hall devices 21 and 22 with a coefficient. Thus, even ifeach hall device contains a magnetic flux disturbance, this disturbancecan be canceled. Therefore, highly accurate output detection is enabled.Meanwhile, calculation on the above described currents I₁, I₂, I₃ iscarried out by the operation processing circuit 30.

Next, a current amplification factor will be obtained. Magnetic field B₁received by the first hall device 21 near I₁ from the conductor currentI₁ is expressed by Expression 11. $\begin{matrix}{B_{1} = {{{- \frac{1}{4\quad \pi \quad r}}\left( {1 + \frac{1}{\sqrt{2}}} \right)I_{1}} = {- {f\left( I_{1} \right)}}}} & \left\lbrack {{Expression}\quad 11} \right\rbrack\end{matrix}$

Current I₁ is expressed by Expression 12 from equation (13).$\begin{matrix}\begin{matrix}{I_{1} = \quad {{\frac{1}{2}\quad \pi \quad {r\left( {{- B_{1}} - B_{2} + B_{3} + B_{4}} \right)}} - {2\left( {\sqrt{2} - 1} \right)\pi \quad {r\left( {B_{2} - B_{1}} \right)}}}} \\{= \quad {{\frac{1}{2 \cdot \frac{1}{\pi \quad r}}\quad \left( {{- B_{1}} - B_{2} + B_{3} + B_{4}} \right)} -}} \\{\quad {\frac{1}{\frac{1}{\sqrt{2} - 1} \cdot \frac{1}{2\pi \quad r}}\quad \left( {B_{2} - B_{1}} \right)}} \\{= \quad {{\frac{1}{{4 \cdot \frac{2\sqrt{2}}{\sqrt{2} + 1} \cdot \frac{1}{4\pi \quad r}}\left( {1 + \frac{1}{\sqrt{2}}} \right)}\quad \left( {{- B_{1}} - \quad B_{2} + \quad B_{3} + \quad B_{4}} \right)}\quad -}} \\{\quad {\frac{1}{{\frac{1}{\sqrt{2} - 1} \cdot \frac{2\sqrt{2}}{\sqrt{2} + 1} \cdot \frac{1}{4\pi \quad r}}\left( {1 + \frac{1}{\sqrt{2}}} \right)}\left( {B_{2} - B_{1}} \right)}}\end{matrix} & \left\lbrack {{Expression}\quad 12} \right\rbrack\end{matrix}$

Therefore, Expression 13 is established about current I₁.

[Expression 13]

1/4(−B ₁ −B ₂ +B ₃ +B ₄)−({square root over (2)}−1)(B ₂ −B ₁)=−2({squareroot over (2)}−2)f(I ₁)

If current I₃ is obtained like current I₁, Expression 14 is establishedabout current I₃.

[Expression 14]

1/4(−B ₁ −B ₂ +B ₃ +B ₄)+({square root over (2)}−1)(B ₂ −B ₁)=−2({squareroot over (2)}−2)f(I₃)

Further, current I₂ is expressed by Expression 15 from equation (7).$\begin{matrix}\begin{matrix}{I_{2} = \quad {{{- \frac{2\sqrt{2}}{\sqrt{2} + 2}} \cdot \pi}\quad {r\left( {B_{2} - B_{1}} \right)}}} \\{= \quad {{- \frac{1}{\left( {\sqrt{2} + 2} \right) \cdot \frac{1}{2\quad \pi \quad r} \cdot \frac{1}{\sqrt{2}}}}\quad \left( {B_{2} - B_{1}} \right)}} \\{= \quad {{- \frac{1}{\frac{2\left( {\sqrt{2} + 2} \right)}{\sqrt{2} + 1} \cdot \frac{1}{4\pi \quad r} \cdot \left( {1 + \frac{1}{\sqrt{2}}} \right)}}\quad \left( {B_{2} - B_{1}} \right)}}\end{matrix} & \left\lbrack {{Expression}\quad 15} \right\rbrack\end{matrix}$

Therefore, Expression 16 is established about current I₂.$\begin{matrix}{{B_{2} - B_{1}} = {{{- \frac{2\left( {\sqrt{2} + 2} \right)}{\sqrt{2} + 1}}\quad {f\left( I_{2} \right)}} = {{- 2}\sqrt{2}{f\left( I_{2} \right)}}}} & \left\lbrack {{Expression}\quad 16} \right\rbrack\end{matrix}$

Consequently, it is possible to obtain a sensitivity 1.2 times or 1.4times a sensitivity received by a single hall device located nearest asingle measuring object conductor. Thus, a high sensitivity currentmeasurement is enabled.

Seventh Embodiment

The seventh embodiment has a feature that it is capable of obtaining acurrent at a better accuracy than the current detecting apparatus of thethird embodiment. Because the current detecting apparatus of the seventhembodiment is of the same structure as the current detecting apparatusshown in FIGS. 12, 13, an operation thereof will be described.

Here, the magnetism sensitive surface is disposed such that a magneticfield penetrating vertically beyond a paper face to the other side ispositive. The four hall devices 21-24 are disposed at the same distanceto the conductors which sandwich each of the hall devices. The distanceis r.

Four variables, currents I₁-I₄ flowing through the four conductors 11-14are obtained according to an equation obtained from four hall devices21-24 and Kirchhoff formula.

First, magnetic flux B₁ received by the first hall device 21 isexpressed by Expression 17. $\begin{matrix}{B_{1} = {{\frac{1}{4\pi \quad r}\left\lbrack {{\left( {1 + {\cos \quad \frac{\pi}{4}}} \right)I_{1}} - {\left( {1 + {\cos \quad \frac{\pi}{4}}} \right)I_{2}} - {\left( {1 + {\cos \quad \frac{3\pi}{4}}} \right)I_{3}} + {\left( {1 + {\cos \quad \frac{3\pi}{4}}} \right)I_{4}}} \right\rbrack} = {{\frac{1}{4\sqrt{2}\quad \pi \quad r}\left\lbrack {{\left( {1 + \sqrt{2}} \right)I_{1}} - \quad {\left( {1 + \sqrt{2}} \right)I_{2}} - {\left( {\sqrt{2} - 1} \right)I_{3}} + {\left( {\sqrt{2} - 1} \right)I_{4}}} \right\rbrack}}}} & \left\lbrack {{Expression}\quad 17} \right\rbrack\end{matrix}$

A first term of Expression 17 indicates a magnetic flux received fromcurrent I₁ and a second term indicates a magnetic flux received fromcurrent I₂ and a third term indicates a magnetic flux received fromcurrent I₃ and a fourth term indicates a magnetic flux received fromcurrent I₄.

If a magnetic flux B₂ received by the second hall device 22 is obtainedin the same manner as a magnetic flux received by the first hall device21, magnetic flux B₂ is expressed by Expression 18. $\begin{matrix}{B_{2} = {{\frac{1}{4\pi \quad r}\left\lbrack {{\left( {1 + {\cos \quad \frac{3\pi}{4}}} \right)I_{1}} + {\left( {1 + {\cos \quad \frac{\pi}{4}}} \right)I_{2}} - {\left( {1 + {\cos \quad \frac{\pi}{4}}} \right)I_{3}} - {\left( {1 + {\cos \quad \frac{3\pi}{4}}} \right)I_{4}}} \right\rbrack} = {{\frac{1}{4\sqrt{2}\quad \pi \quad r}\left\lbrack {{\left( {\sqrt{2} - 1} \right)I_{1}} + \quad {\left( {\sqrt{2} + 1} \right)I_{2}} - {\left( {\sqrt{2} + 1} \right)I_{3}} - {\left( {\sqrt{2} - 1} \right)I_{4}}} \right\rbrack}}}} & \left\lbrack {{Expression}\quad 18} \right\rbrack\end{matrix}$

A magnetic field B₃ received by the third hall device is expressed byExpression 19. $\begin{matrix}{B_{3} = {{\frac{1}{4\pi \quad r}\left\lbrack {{{- \left( {1 + {\cos \quad \frac{3\pi}{4}}} \right)}I_{1}} + {\left( {1 + {\cos \quad \frac{3\pi}{4}}} \right)I_{2}} + {\left( {1 + {\cos \quad \frac{\pi}{4}}} \right)I_{3}} - {\left( {1 + {\cos \quad \frac{\pi}{4}}} \right)I_{4}}} \right\rbrack} = {{\frac{1}{4\sqrt{2}\quad \pi \quad r}\left\lbrack {{\left( {{- \sqrt{2}} + 1} \right)I_{1}} + \quad {\left( {\sqrt{2} - 1} \right)I_{2}} + {\left( {\sqrt{2} + 1} \right)I_{3}} - {\left( {\sqrt{2} + 1} \right)I_{4}}} \right\rbrack}}}} & \left\lbrack {{Expression}\quad 19} \right\rbrack\end{matrix}$

A magnetic field B₄ received by the fourth hall device 24 is expressedby Expression 20. $\begin{matrix}{B_{4} = {{\frac{1}{4\pi \quad r}\left\lbrack {{{- \left( {1 + {\cos \quad \frac{\pi}{4}}} \right)}I_{1}} - {\left( {1 + {\cos \quad \frac{3\pi}{4}}} \right)I_{2}} + {\left( {1 + {\cos \quad \frac{3\pi}{4}}} \right)I_{3}} + {\left( {1 + {\cos \quad \frac{\pi}{4}}} \right)I_{4}}} \right\rbrack} = {{\frac{1}{4\sqrt{2}\quad \pi \quad r}\left\lbrack {{\left( {{- \sqrt{2}} - 1} \right)I_{1}} + \quad {\left( {{- \sqrt{2}} + 1} \right)I_{2}} + {\left( {\sqrt{2} - 1} \right)I_{3}} + {\left( {\sqrt{2} + 1} \right)I_{4}}} \right\rbrack}}}} & \left\lbrack {{Expression}\quad 20} \right\rbrack\end{matrix}$

Expression 21 is established from the above equations. $\begin{matrix}{{{4\sqrt{2}\quad \pi \quad {r\begin{pmatrix}B_{1} \\B_{2} \\B_{3} \\B_{4}\end{pmatrix}}} = {\begin{pmatrix}{\sqrt{2} + 1} & {{- \sqrt{2}} - 1} & {{- \sqrt{2}} + 1} & {\sqrt{2} - 1} \\{\sqrt{2} - 1} & {\sqrt{2} + 1} & {{- \sqrt{2}} - 1} & {{- \sqrt{2}} + 1} \\{{- \sqrt{2}} + 1} & {\sqrt{2} - 1} & {\sqrt{2} + 1} & {{- \sqrt{2}} - 1} \\{{- \sqrt{2}} - 1} & {{- \sqrt{2}} + 1} & {\sqrt{2} - 1} & {\sqrt{2} + 1}\end{pmatrix}\quad \begin{pmatrix}I_{1} \\I_{2} \\I_{3} \\I_{4}\end{pmatrix}}}{A = \begin{pmatrix}{\sqrt{2} + 1} & {{- \sqrt{2}} - 1} & {{- \sqrt{2}} + 1} & {\sqrt{2} - 1} \\{\sqrt{2} - 1} & {\sqrt{2} + 1} & {{- \sqrt{2}} - 1} & {{- \sqrt{2}} + 1} \\{{- \sqrt{2}} + 1} & {\sqrt{2} - 1} & {\sqrt{2} + 1} & {{- \sqrt{2}} - 1} \\{{- \sqrt{2}} - 1} & {{- \sqrt{2}} + 1} & {\sqrt{2} - 1} & {\sqrt{2} + 1}\end{pmatrix}}{{\det (A)} = {{\left( {\sqrt{2} + 1} \right)^{4} + \left( {{- \sqrt{2}} - 1} \right)^{4} + \left( {{- \sqrt{2}} + 1} \right)^{4} + \left( {\sqrt{2} - 1} \right)^{4} - {2\left( {\sqrt{2} + 1} \right)^{2}\left( {{- \sqrt{2}} + 1} \right)^{2}} - {2\left( {{- \sqrt{2}} - 1} \right)^{2}\left( {\sqrt{2} - 1} \right)^{2}}} = 64}}} & \left\lbrack {{Expression}\quad 21} \right\rbrack\end{matrix}$

A₁-A₄ are defined by Expression 22. $\begin{matrix}{{A_{1} = \begin{pmatrix}{4\sqrt{2}\quad \pi \quad r\quad B_{1}} & {{- \sqrt{2}} - 1} & {{- \sqrt{2}} + 1} & {\sqrt{2} - 1} \\{4\sqrt{2}\quad \pi \quad r\quad B_{2}} & {\sqrt{2} + 1} & {{- \sqrt{2}} - 1} & {{- \sqrt{2}} + 1} \\{4\sqrt{2}\quad \pi \quad r\quad B_{3}} & {\sqrt{2} - 1} & {\sqrt{2} + 1} & {{- \sqrt{2}} - 1} \\{4\sqrt{2}\quad \pi \quad r\quad B_{4}} & {{- \sqrt{2}} + 1} & {\sqrt{2} - 1} & {\sqrt{2} + 1}\end{pmatrix}}{A_{2} = \begin{pmatrix}{\sqrt{2} + 1} & {4\sqrt{2}\quad \pi \quad r\quad B_{1}} & {{- \sqrt{2}} + 1} & {\sqrt{2} - 1} \\{\sqrt{2} - 1} & {4\sqrt{2}\quad \pi \quad r\quad B_{2}} & {{- \sqrt{2}} - 1} & {{- \sqrt{2}} + 1} \\{{- \sqrt{2}} + 1} & {4\sqrt{2}\quad \pi \quad r\quad B_{3}} & {\sqrt{2} + 1} & {{- \sqrt{2}} - 1} \\{{- \sqrt{2}} - 1} & {4\sqrt{2}\quad \pi \quad r\quad B_{4}} & {\sqrt{2} - 1} & {\sqrt{2} + 1}\end{pmatrix}}{A_{3} = \begin{pmatrix}{\sqrt{2} + 1} & {{- \sqrt{2}} - 1} & {4\sqrt{2}\quad \pi \quad r\quad B_{1}} & {\sqrt{2} - 1} \\{\sqrt{2} - 1} & {\sqrt{2} + 1} & {4\sqrt{2}\quad \pi \quad r\quad B_{2}} & {{- \sqrt{2}} + 1} \\{{- \sqrt{2}} + 1} & {\sqrt{2} - 1} & {4\sqrt{2}\quad \pi \quad r\quad B_{3}} & {{- \sqrt{2}} - 1} \\{{- \sqrt{2}} - 1} & {{- \sqrt{2}} + 1} & {4\sqrt{2}\quad \pi \quad r\quad B_{4}} & {\sqrt{2} + 1}\end{pmatrix}}{A_{4} = \begin{pmatrix}{\sqrt{2} + 1} & {{- \sqrt{2}} - 1} & {{- \sqrt{2}} + 1} & {4\sqrt{2}\quad \pi \quad r\quad B_{1}} \\{\sqrt{2} - 1} & {\sqrt{2} + 1} & {{- \sqrt{2}} - 1} & {4\sqrt{2}\quad \pi \quad r\quad B_{2}} \\{{- \sqrt{2}} + 1} & {\sqrt{2} - 1} & {\sqrt{2} + 1} & {4\sqrt{2}\quad \pi \quad r\quad B_{3}} \\{{- \sqrt{2}} - 1} & {{- \sqrt{2}} + 1} & {\sqrt{2} - 1} & {4\sqrt{2}\quad \pi \quad r\quad B_{4}}\end{pmatrix}}} & \left\lbrack {{Expression}\quad 22} \right\rbrack\end{matrix}$

Expression 21 is solved using Cramer's rule to obtain respectivecurrents. Current I₁ is obtained according to Expression 23.$\begin{matrix}\begin{matrix}{I_{1} = \quad \frac{\det \left( A_{1} \right)}{\det (A)}} \\{= \quad {{{\frac{4\sqrt{2}\quad \pi \quad r}{64}{\left\{ {\left\lbrack {\left( {\sqrt{2} + 1} \right)^{3} - {\left( {{- \sqrt{2}} + 1} \right)^{2}\quad \left( {\sqrt{2} + \quad 1} \right)}} \right\rbrack \quad B_{1}} \right.}}} +}} \\{\quad {{{\left\lbrack {\left( {\sqrt{2} - 1} \right)^{3} - {\left( {{- \sqrt{2}} - 1} \right)^{2}\quad \left( {\sqrt{2} - 1} \right)}} \right\rbrack \quad B_{2}} +}}} \\{\quad {{{\left\lbrack {\left( {{- \sqrt{2}} + 1} \right)^{3} - {\left( {\sqrt{2} + 1} \right)^{2}\left( {{- \sqrt{2}} + 1} \right)}} \right\rbrack B_{3}} +}}} \\{\quad \left. {\left\lbrack {\left( {{- \sqrt{2}} - 1} \right)^{3} - \quad {\left( {\sqrt{2} - 1} \right)^{2}\quad \left( {{- \sqrt{2}} - 1} \right)}} \right\rbrack B_{4}}\quad \right\} \quad} \\{{{= \quad {{{\frac{\pi \quad r}{2}\left\lbrack {\left( {\sqrt{2} + 1} \right)B_{1}} \right.}} + {\left( {{- \sqrt{2}} + 1} \right)B_{2}}}}} +} \\\left. {{{\quad {\left( {\sqrt{2} - 1} \right)B_{3}}} + {\left( {{- \sqrt{2}} - 1} \right)B_{4}}}} \right\rbrack \\{= \quad {\left. {\frac{\pi \quad r}{2}\left\lbrack {{\left( {\sqrt{2} - 1} \right)\quad \left( {B_{3} - B_{2}} \right)} + \quad {{\left( {\sqrt{2} + \quad 1} \right)\quad \left( {B_{1} - B_{4}} \right)}}} \right.} \right\rbrack }}\end{matrix} & \left\lbrack {{Expression}\quad 23} \right\rbrack\end{matrix}$

Likewise, current I₂ is obtained by Expression 24. $\begin{matrix}\begin{matrix}{{{I_{2} = \quad {{\frac{\pi \quad r}{2}\left\lbrack {\left( {{- \sqrt{2}} - 1} \right)B_{1}} \right.} + {\left( {\sqrt{2} + 1} \right)B_{2}}}}} +} \\\left. {{{\quad {\left( {{- \sqrt{2}} + 1} \right)B_{3}}} + {\left( {\sqrt{2} - 1} \right)B_{4}}}} \right\rbrack \\{{= \quad {\frac{\pi \quad r}{2}\left\lbrack {{\left( {\sqrt{2} - 1} \right)\quad \left( {B_{4} - B_{3}} \right)} + \quad {{\left( {\sqrt{2} + \quad 1} \right)\quad \left( {B_{2} - B_{1}} \right)}}} \right\rbrack}}}\end{matrix} & \left\lbrack {{Expression}\quad 24} \right\rbrack\end{matrix}$

Likewise, both currents 13 and 14 are obtained by Expression 25.$\begin{matrix}\begin{matrix}{{{I_{3} = \quad {{\frac{\pi \quad r}{2}\left\lbrack {\left( {\sqrt{2} - 1} \right)B_{1}} \right.} + {\left( {{- \sqrt{2}} - 1} \right)B_{2}}}}} +} \\\left. {{{\quad {\left( {\sqrt{2} + 1} \right)B_{3}}} + {\left( {{- \sqrt{2}} + 1} \right)B_{4}}}} \right\rbrack \\{{= \quad {\frac{\pi \quad r}{2}\left\lbrack {{\left( {\sqrt{2} - 1} \right)\quad \left( {B_{1} - B_{4}} \right)} + \quad {{\left( {\sqrt{2} + \quad 1} \right)\quad \left( {B_{3} - B_{2}} \right)}}} \right\rbrack}}} \\{{{I_{4} = \quad {{\frac{\pi \quad r}{2}\left\lbrack {\left( {{- \sqrt{2}} + 1} \right)B_{1}} \right.} + {\left( {\sqrt{2} - 1} \right)B_{2}}}}} +} \\\left. {{{\quad {\left( {{- \sqrt{2}} - 1} \right)B_{3}}} + {\left( {\sqrt{2} + 1} \right)B_{4}}}} \right\rbrack \\{{= \quad {\frac{\pi \quad r}{2}\left\lbrack {{\left( {\sqrt{2} - 1} \right)\quad \left( {B_{2} - B_{1}} \right)} + \quad {{\left( {\sqrt{2} + \quad 1} \right)\quad \left( {B_{4} - B_{3}} \right)}}} \right\rbrack}}}\end{matrix} & \left\lbrack {{Expression}\quad 25} \right\rbrack\end{matrix}$

As described above, currents I₁-I₄ can be calculated by multiplying adifference between magnetic fields received by two hall devices with acoefficient. Thus, even if the respective hall devices contain magneticflux disturbance; this disturbance can be canceled, so that a highlyaccurate output detection is enabled. The above described currents I₁-I₄are calculated by the operation processing circuit 30.

Next, a current amplification factor will be obtained. Current I₁ isexpressed by Expression 26. $\begin{matrix}{{{I_{1} = {\frac{\pi \quad r}{2}\left\lbrack {{\left( {\sqrt{2} - 1} \right)\quad \left( {B_{3} - B_{2}} \right)} + \quad {{\left( {\sqrt{2} + \quad 1} \right)\quad \left( {B_{1} - B_{4}} \right)}}} \right\rbrack}}}\begin{matrix}{I_{1} = \quad {{\frac{1}{\frac{2}{\pi \quad r} \cdot \frac{1}{\sqrt{2} - 1}}\left( {B_{3} - B_{2}} \right)} + {\frac{1}{\frac{2}{\pi \quad r} \cdot \frac{1}{\sqrt{2} + 1}}\left( {B_{1} - B_{4}} \right)}}} \\{= \quad {{\frac{1}{\frac{8}{4\pi \quad r} \cdot \left( {\sqrt{2} + 1} \right)}\left( {B_{3} - B_{2}} \right)} + {\frac{1}{\frac{8}{4\pi \quad r} \cdot \left( {\sqrt{2} - 1} \right)}\left( {B_{1} - B_{4}} \right)}}} \\{= \quad {{\frac{1}{8{\sqrt{2} \cdot \frac{1}{4\pi \quad r} \cdot \left( {1 + \frac{1}{\sqrt{2}}} \right)}}\left( {B_{3} - B_{2}} \right)} +}} \\{\quad {\frac{1}{8{\sqrt{2} \cdot \frac{\sqrt{2} - 1}{\sqrt{2} + 1} \cdot \frac{1}{4\pi \quad r} \cdot \left( {1 + \frac{1}{\sqrt{2}}} \right)}}\left( {B_{1} - B_{4}} \right)}}\end{matrix}} & \left\lbrack {{Expression}\quad 26} \right\rbrack\end{matrix}$

A magnetic flux B, is defined by Expression 27. $\begin{matrix}{B_{1} = {{\frac{1}{4\quad \pi \quad r}\left( {1 + \frac{1}{\sqrt{2}}} \right)I_{1}} = {f\left( I_{1} \right)}}} & \left\lbrack {{Expression}\quad 27} \right\rbrack\end{matrix}$

If Expression 26 is transformed by using Expression 27, Expression 28 isobtained. $\begin{matrix}{{B_{3} - B_{2} + {\frac{\sqrt{2} + 1}{\sqrt{2} - 1}\left( {B_{1} - B_{4}} \right)}} = {8\sqrt{2}{f\left( I_{1} \right)}}} & \left\lbrack {{Expression}\quad 28} \right\rbrack\end{matrix}$

As a result of operation based on Expression 28, a sensitivity about11.3 times a sensitivity received by a single hall device locatednearest a single measuring object conductor is obtained from thatmeasuring object conductor. Thus, a highly accurate current measurementis enabled.

Eighth Embodiment

The eighth embodiment has a feature that it is capable of obtaining acurrent at a better accuracy than the current detecting apparatus of thefourth embodiment. Because the current detecting apparatus of the eighthembodiment is of the same structure as the current detecting apparatusshown in FIGS. 14, 15, an operation thereof will be described.

An equation based on expression 29 is established about variables,currents I₁-I₃ and magnetic fields B₁-B₃ according to Biot—Savart's law.$\begin{matrix}{{B_{1} = {{\frac{1}{4\quad \pi \quad r}\left\lbrack {{{- \left( {1 + \frac{1}{\sqrt{2}}} \right)}I_{1}} + {\left( {1 + \frac{1}{\sqrt{2}}} \right)I_{2}}} \right\rbrack}\quad (1)}}{B_{2} = {{\frac{1}{4\quad \pi \quad r}\left\lbrack {{{- \left( {1 - \frac{1}{\sqrt{2}}} \right)}I_{1}} - {\left( {1 + \frac{1}{\sqrt{2}}} \right)I_{2}}} \right\rbrack}\quad (2)}}{B_{3} = {{\frac{1}{4\quad \pi \quad r}\left\lbrack {{\left( {1 + \frac{1}{\sqrt{2}}} \right)I_{1}} + {\left( {1 - \frac{1}{\sqrt{2}}} \right)I_{2}}} \right\rbrack}\quad (3)}}{0 = {I_{1} + I_{2} + {I_{3}\quad (4)}}}} & \left\lbrack {{Expression}\quad 29} \right\rbrack\end{matrix}$

If equation (1) is subtracted from equation (3) of Expression 29,Expression 30 is obtained.

[Expression 30]

4{square root over (2)}πr(B ₃ −B ₁)=2({square root over (2)}+1)I ₁−2I₂  (5)

Further, if equation (1) is subtracted from equation (2) of Expression29, Expression 31 is obtained.

[Expression 31]

4{square root over (2)}πr(B ₂ −B ₁)=2I ₁−2({square root over (2)}+1)I₂  (6)

If both sides of equation (6) of Expression 31 are multiplied by(2^(1/2)+1) times, Expression 32 is obtained.

[Expression 32]

4({square root over (2)}+2)πr(B ₂ −B ₁)=2({square root over (2)}+1)I₁−2({square root over (2)}+1)² I ₂  (7)

If equation (5) is subtracted from equation (7) of Expression 32,Expression 33 is obtained.

[Expression 33]

πr[−8S ₁+(4{square root over (2)}+8)B ₂−4{square root over (2)}B₃]=−(4+4{square root over (2)})I ₂

Thus, current I₂ is expressed by Expression 34. $\begin{matrix}\begin{matrix}{I_{2} = {- \frac{\pi \quad {r\left\lbrack {{{- 2}B_{1}} + {\left( {\sqrt{2} + 2} \right)B_{2}} - {\sqrt{2}B_{3}}} \right\rbrack}}{\sqrt{2} + 1}}} \\{= {\pi \quad {r\left\lbrack {{\left( {{2\sqrt{2}} - 2} \right)B_{1}} + {\sqrt{2}B_{2}} + {\left( {\sqrt{2} - 2} \right)B_{3}}} \right\rbrack}}} \\{= {\pi \quad {r\left\lbrack {{\sqrt{2}\left( {B_{2} - B_{1}} \right)} + {\left( {\sqrt{2} - 2} \right)\left( {B_{3} - B_{1}} \right)}} \right\rbrack}\quad (8)}}\end{matrix} & \left\lbrack {{Expression}\quad 34} \right\rbrack\end{matrix}$

Further, if equation (8) is substituted into equation (6), Expression 35is obtained to obtain current I₁.

[Expression 35]

I ₁ =πr[(2−2{square root over (2)})B ₁+({square root over (2)}−2)B₂+{square root over (2)}B ₃ ]=πr[{square root over (2)}(B ₃ −B₁)+({square root over (2)}−2)(B ₂ −B ₁)]  (9)

Further, if equation (2) is added to equation (1), Expression 36 isobtained.

[Expression 36]

4{square root over (2)}πr(B ₁ +B ₂)=−2{square root over (2)}I ₁  (10)

4{square root over (2)}πr(B ₁ +B ₃)=2{square root over (2)}I ₂  (11)

Further, if equations (10), (11) are substituted into equation (4),Expression 37 is obtained to obtain current I3.

[Expression 37]

I ₃ =−I ₁ −I ₂=2πr(B ₂ −B ₃)

As described above, currents I₁, I₂, I₃ can be calculated by multiplyinga difference between magnetic fields received by two hall devices with acoefficient. Thus, because even if the respective hall devices containthe magnetic flux disturbance, this disturbance can be canceled, ahighly accurate output detection is enabled. Meanwhile, the abovedescribed currents I₁, I₂, I₃ are calculated by the operation processingcircuit 30.

Ninth Embodiment

This ninth embodiment has a feature that it is capable of obtaining acurrent at a better accuracy than the current detecting apparatus of thefifth embodiment. Because the current detecting apparatus of the ninthembodiment is of the same configuration as the current detectingapparatus shown in FIGS. 16, 17, an operation thereof will be described.

An equation based on Expression 38 is established about variables,currents I_(i)-I₄ and magnetic fields B_(i)-B₄ because of Biot—Savart'slaw. $\begin{matrix}{{B_{1} = {{\frac{1}{4\quad \pi \quad r}\left\lbrack {{\left( {1 + \frac{1}{\sqrt{2}}} \right)I_{2}} - {\left( {1 + \frac{1}{\sqrt{2}}} \right)I_{1}} + {\left( {1 - \frac{1}{\sqrt{2}}} \right)I_{3}}} \right\rbrack}\quad (1)}}{B_{2} = {{{{\frac{1}{4\pi \quad r}\left\lbrack {{{- \left( {1 + \frac{1}{\sqrt{2}}} \right)}I_{2}} - {\left( {1 - \frac{1}{\sqrt{2}}} \right)I_{1}} + {\left( {1 + \frac{1}{\sqrt{2}}} \right)I_{3}}} \right\rbrack}\quad (2)B_{3}} = {{{{\frac{1}{4\pi \quad r}\left\lbrack {{{- \left( {1 - \frac{1}{\sqrt{2}}} \right)}I_{2}} + {\left( {1 - \frac{1}{\sqrt{2}}} \right)I_{1}} - {\left( {1 + \frac{1}{\sqrt{2}}} \right)I_{3}}} \right\rbrack}\quad (3)\quad B_{4}} = {{{{\frac{1}{4\pi \quad r}\left\lbrack {{\left( {1 - \frac{1}{\sqrt{2}}} \right)I_{2}} + {\left( {1 + \frac{1}{\sqrt{2}}} \right)I_{1}} - {\left( {1 - \frac{1}{\sqrt{2}}} \right)I_{3}}} \right\rbrack}\quad (4)0} = {I_{1} + I_{2} + I_{3} + {I_{4}\quad (5)}}}}}}}}}} & \left\lbrack {{Expression}\quad 38} \right\rbrack\end{matrix}$

Because Expression 38 has five equations for four variables, itssolution is not single. It is necessary to obtain a solution capable ofcanceling disturbance noise. First, currents I_(i)-I₃ are obtainedaccording to equations (1)-(4) of Expression 38 and then the obtainedcurrent I_(i) is substituted into the equation (5) to obtain current I₄.

First, equation (1)−equation (2)−equation (3)+equation (4) is operatedto obtain Expression 39. Then, current I₂ is obtained. $\begin{matrix}{{{B_{2} - B_{3} - B_{4} + B_{1}} = {\frac{1}{\pi \quad r}I_{2}}}{I_{2} = {\pi \quad {r\left( {B_{2} - B_{3} - B_{4} + B_{1}} \right)}}}} & \left\lbrack {{Expression}\quad 39} \right\rbrack\end{matrix}$

Next, equation (4) is subtracted from equation (1) to obtain Expression40.

[Expression 40]

4{square root over (2)}πr(B ₂ −B ₁)=2{square root over (2)}I ₂−2({squareroot over (2)}+1)I ₁=2{square root over (2)}πr(B ₂ −B ₃ −B ₄ +B₁)−2({square root over (2)}+1)I ₁

Therefore, current I₁ is expressed by Expression 41. $\begin{matrix}{I_{1} = \frac{\sqrt{2}\pi \quad {r\left( {{- B_{2}} - B_{3} - B_{4} + {3B_{1}}} \right)}}{\sqrt{2} + 1}} & \left\lbrack {{Expression}\quad 41} \right\rbrack\end{matrix}$

Likewise, current I₃ and current I₄ are expressed by expression 42.$\begin{matrix}{{I_{3} = \frac{\sqrt{2}\pi \quad {r\left( {B_{2} + B_{3} - {3B_{4}} + B_{1}} \right)}}{\sqrt{2} + 1}}{I_{4} = {{- \left( {I_{1} + I_{2} + I_{3}} \right)} = {{{{- \pi}\quad {rB}_{2}} + {\pi \quad {rB}_{3}} + {\left( {1 + \frac{\sqrt{2}}{\sqrt{2} + 1} + \frac{3\sqrt{2}}{\sqrt{2} + 1}} \right)\pi \quad {rB}_{4}} - {\left( {1 + \frac{3\sqrt{2}}{\sqrt{2} + 1} + \frac{\sqrt{2}}{\sqrt{2} + 1}} \right)\pi \quad {rB}_{1}}} = {\pi \quad {r\left\lbrack {B_{3} - B_{2} + {\frac{{5\sqrt{2}} + 1}{\sqrt{2} + 1}\left( {B_{4} - B_{1}} \right)}} \right\rbrack}}}}}} & \left\lbrack {{Expression}\quad 42} \right\rbrack\end{matrix}$

As shown above, currents I₁-I₄ can be calculated by multiplying adifference between magnetic fields received by two hall devices with acoefficient. Thus, even if the respective hall devices include magneticflux disturbance, this disturbance can be canceled. Thus, a highlyaccurate output detection is enabled. Meanwhile, the above calculationson the currents I₁-I₄ are carried out by the operation processingcircuit 30.

Tenth Embodiment

According to the tenth embodiment, n of the present invention is “3” andm is “2”. Tow angles of three angles formed by the first-thirdconductors are equal while the remaining one is different from theaforementioned two angles. FIG. 19 is a perspective view showing astructure of a sensor portion of the current detecting apparatusaccording to the tenth embodiment. This sensor portion is comprised ofthe conductor 10, first hall device 21, and second hall device 22.Usually, these components are incorporated in an electric connection box(not shown). In this first embodiment, no magnetism collecting core isused.

As shown in FIG. 19, the conductor 10 is comprised of the firstconductor 11, second conductor 12 and third conductor 13 disposed inthree directions from the branch point O on a flat plane including thebranch point O. The first conductor 11, second conductor 12 and thethird conductor 12 correspond to n conductors of the present invention.Ends of the respective conductors are connected to the branch point O.

In the meantime, the conductor 10 may be composed by connecting ends ofthe three separate conductors, namely, the first conductor 11, secondconductor 12 and third conductor 13 at the branch point O and instead byforming integrally the first conductor 11, second conductor 12 and thirdconductor 13. Further, it is also permissible to compose this conductor10 by forming a wiring pattern having three branch routes including thefirst conductor 11, second conductor 12 and third conductor 13 on asubstrate.

The first hall device 21 and second hall device 22 correspond to melectromagnetic transducers of the present invention. Each hall devicegenerates a voltage (hall voltage) signal corresponding to a density ofmagnetic flux entering its magnetism sensitive surface. A predeterminedcurrent is supplied to each hall device through a lead (not shown) andthe voltage signal generated in each hall device is fetched out througha lead (not shown).

Positions where the respective hall devices are disposed are determinedas follows. That is, the first hall device 21 is disposed between thefirst conductor 11 and the second conductor 12 and at the same distancefrom these conductors. The second hall device 22 is disposed between thefirst conductor 11 and the third conductor 13 and at the same distancefrom these conductors. The magnetism sensitive surfaces of therespective hall devices substantially coincide with the plane includingthe branch point O and are disposed such that they are directed in thesame direction.

Next, an operation of the sensor portion of the current detectingapparatus according to the tenth embodiment of the present inventionhaving such a structure will be described.

Assume that a current flowing through the first conductor 11 which is ameasuring object conductor is I₁, a current flowing through the secondconductor 12 after branch is I₂ and a current flowing through the thirdconductor 13 is I₃. Then, assume that an angle between the secondconductor 12 and the third conductor 13 is 74 ₁, an angle between thefirst conductor 11 and the second conductor 12 is θ₂, and an anglebetween the first conductor 11 and the third conductor 13 is 74 ₃. Atthis time, Expression 43 is established. $\begin{matrix}{\theta_{2} = {\theta_{3} = {{\frac{1}{2}\left( {{2\quad \pi}\overset{\cdot}{-}\theta_{1}} \right)} = {\pi - {\frac{1}{2}\theta_{1}\quad (1)}}}}} & \left\lbrack {{Expression}\quad 43} \right\rbrack\end{matrix}$

At this time, Expression 44 is established because of Kirchhoff formula.

[Expression 44]

I ₁ +I ₂ +I ₃=0  (2)

Next, calculation of magnetic fields received by the hall devices 21; 22will be described. First, calculation of the magnetic field received bythe first hall device 21 will be described with reference to FIG. 19.The magnetic field received by the first hall device is calculated forevery current. A magnetic field which the first hall device 21 receivesfrom the current I₁ is expressed by Expression 45. $\begin{matrix}{\frac{I_{1}}{4\quad \pi \quad r}\left( {{\cos \quad \frac{\theta_{2}}{2}} + {\cos \quad \theta^{\prime}}} \right)} & \left\lbrack {{Expression}\quad 45} \right\rbrack\end{matrix}$

Where θ′ is an angle formed by the first conductor 11 and a line formedby the left end portion of the first conductor 11 and the first halldevice 21, and r is a length of a vertical line from the first halldevice 21 to the first conductor 11. When r is small enough as comparedto the length of the first conductor 11, θ′=0, therefore cos θ′=1.

Thus, the aforementioned magnetic field is expressed by Expression 46.$\begin{matrix}{\frac{I_{1}}{4\quad \pi \quad r}\left( {1 + {\cos \quad \frac{\theta_{2}}{2}}} \right)} & \left\lbrack {{Expression}\quad 46} \right\rbrack\end{matrix}$

Further, Expression 47 is established by equation (1) of Expression 43so that a magnetic field which the first hall device 21 receives fromthe current I₁ is obtained. $\begin{matrix}{{\frac{I_{1}}{4\quad \pi \quad r}\left\{ {1 + {\cos \quad \left( {\frac{1}{2}\left( {\pi - {\frac{1}{2}\quad \theta_{1}}} \right)} \right)}} \right\}} = {{\frac{I_{1}}{4\quad \pi \quad r}\left\{ {1 + {\cos \quad \left( {{\frac{1}{2}\pi} - {\frac{1}{4}\quad \theta_{1}}} \right)}} \right\}} = {{\frac{I_{1}}{4\quad \pi \quad r}\left( {1 + {\cos \quad \frac{1}{2}{\pi \cdot \cos}\frac{1}{4}\quad \theta_{1}} + {\sin \quad \frac{1}{2}{\pi \cdot \sin}\frac{1}{4}\quad \theta_{1}}} \right)} = {\frac{I_{1}}{4\quad \pi \quad r}\left( {1 + {\sin \frac{1}{4}\quad \theta_{1}}} \right)}}}} & \left\lbrack {{Expression}\quad 47} \right\rbrack\end{matrix}$

Like calculation of magnetic field which the first hall device receivesfrom the current I₁, a magnetic field which the first hall device 21receives from the current 12 is calculated. That magnetic field isexpressed by Expression 48. $\begin{matrix}{{- \frac{I_{2}}{4\quad \pi \quad r}}\left( {1 + {\sin \quad \frac{1}{4}\theta_{1}}} \right)} & \left\lbrack {{Expression}\quad 48} \right\rbrack\end{matrix}$

Next, calculation of the magnetic field which the first hall device 21receives from the current I₃ will be described with reference to FIG.20. At this time, the magnetic field is expressed by Expression 49.$\begin{matrix}{\frac{I_{3}}{4\quad \pi \quad r}\left\lbrack {{\cos \quad \left( {\theta_{1} + {\frac{1}{2}\theta_{2}}} \right)} + {\cos \quad \theta^{\prime}}} \right\rbrack} & \left\lbrack {{Expression}\quad 49} \right\rbrack\end{matrix}$

Here, Expression 50 is obtained from equation (1) and cos θ′=1. As aresult, a magnetic field which the first hall device 21 receives fromthe current I₂ is obtained. $\begin{matrix}{{{- \frac{I_{3}}{4\quad \pi \quad r}}\left\{ {1 + {\cos \quad\left\lbrack {\theta_{1} + {\frac{1}{2}\left( {\pi - {\frac{1}{2}\quad \theta_{1}}} \right)}} \right\rbrack}} \right\}} = {{- {\frac{I_{3}}{4\quad \pi \quad r}\left\lbrack {1 + {\cos \quad \left( {{\frac{1}{2}\pi} + {\frac{3}{4}\quad \theta_{1}}} \right)}} \right\rbrack}} = {{{- \frac{I_{3}}{4\quad \pi \quad r}}\left( {1 + {\cos \quad \frac{1}{2}{\pi \cdot \cos}\frac{3}{4}\quad \theta_{1}} - {\sin \quad \frac{1}{2}{\pi \cdot \sin}\frac{3}{4}\quad \theta_{1}}} \right)} = {{- \frac{I_{3}}{4\quad \pi \quad r}}\left( {1 - {\sin \frac{3}{4}\quad \theta_{1}}} \right)}}}} & \left\lbrack {{Expression}\quad 50} \right\rbrack\end{matrix}$

Next, the obtained three magnetic fields are overlapped with each otherso as to obtain the magnitude of a magnetic field which the first halldevice 21 receives. Here, if θ₁>2π/3, because θ₁+θ₂/2>π and a directionof a magnetic field received from I₃ is inverse, operations are carriedout about two cases of 0<θ₁≦2π/3 and 2π/3≦θ₁23 2π separately, thensynthetic magnetic field is obtained.

First, in case of 0<θ₁<2π/3, the synthetic magnetic field is expressedby Expression 51. $\begin{matrix}{{{\frac{1}{4\quad \pi \quad r}\left( {1 + {\sin \quad \frac{1}{4}\quad \theta_{1}}} \right)I_{1}} - {\frac{1}{4\quad \pi \quad r}\left( {1 + {\sin \quad \frac{1}{4}\quad \theta_{1}}} \right)I_{2}} - {\frac{1}{4\quad \pi \quad r}\left( {1 - {\sin \quad \frac{3}{4}\quad \theta_{1}}} \right)I_{3}}} = {\frac{1}{4\quad \pi \quad r}\left\lbrack {I_{1} - I_{2} - I_{3} + {\sin \quad \frac{1}{4}\quad {\theta_{1} \cdot \left( {I_{1} - I_{2}} \right)}} + {\sin \frac{3}{4}\quad {\theta_{1} \cdot I_{3}}}} \right\rbrack}} & \left\lbrack {{Expression}\quad 51} \right\rbrack\end{matrix}$

In case of 2π/3≦θ₁≦2π the synthetic magnetic field is expressed byExpression 52. $\begin{matrix}{{{\frac{1}{4\quad \pi \quad r}\left( {1 + {\sin \quad \frac{1}{4}\quad \theta_{1}}} \right)I_{1}} - {\frac{1}{4\quad \pi \quad r}\left( {1 + {\sin \quad \frac{1}{4}\quad \theta_{1}}} \right)I_{2}} + {\frac{1}{4\quad \pi \quad r}\left( {1 - {\sin \quad \frac{3}{4}\quad \theta_{1}}} \right)I_{3}}} = {\frac{1}{4\quad \pi \quad r}\left\lbrack {I_{1} - I_{2} + I_{3} + {\sin \quad \frac{1}{4}\quad {\theta_{1} \cdot \left( {I_{1} - I_{2}} \right)}} - {\sin \frac{3}{4}\quad {\theta_{1} \cdot I_{3}}}} \right\rbrack}} & \left\lbrack {{Expression}\quad 52} \right\rbrack\end{matrix}$

A synthetic magnetic field which the second hall device receives isobtained like calculation of the synthetic magnetic field which thefirst hall device 21 receives. In case of 0<θ₁≦2π/3, the syntheticmagnetic field is expressed by Expression 53. $\begin{matrix}{{{{- \frac{1}{4\quad \pi \quad r}}\left( {1 + {\sin \quad \frac{1}{4}\quad \theta_{1}}} \right)I_{1}} + {\frac{1}{4\quad \pi \quad r}\left( {1 + {\sin \quad \frac{1}{4}\quad \theta_{1}}} \right)I_{3}} + {\frac{1}{4\quad \pi \quad r}\left( {1 - {\sin \quad \frac{3}{4}\quad \theta_{1}}} \right)I_{2}}} = {\frac{1}{4\quad \pi \quad r}\left\lbrack {{- I_{1}} + I_{2} + I_{3} + {\sin \quad \frac{1}{4}\quad {\theta_{1} \cdot \left( {{- I_{1}} + I_{3}} \right)}} - {\sin \frac{3}{4}\quad {\theta_{1} \cdot I_{2}}}} \right\rbrack}} & \left\lbrack {{Expression}\quad 53} \right\rbrack\end{matrix}$

In case of 2θ/3≦θ₁≦2θ, the synthetic magnetic field is expressed byExpression 54. $\begin{matrix}{{{{- \frac{1}{4\quad \pi \quad r}}\left( {1 + {\sin \quad \frac{1}{4}\quad \theta_{1}}} \right)I_{1}} + {\frac{1}{4\quad \pi \quad r}\left( {1 + {\sin \quad \frac{1}{4}\quad \theta_{1}}} \right)I_{3}} - {\frac{1}{4\quad \pi \quad r}\left( {1 - {\sin \quad \frac{3}{4}\quad \theta_{1}}} \right)I_{2}}} = {\frac{1}{4\quad \pi \quad r}\left\lbrack {{- I_{1}} - I_{2} + I_{3} + {\sin \quad \frac{1}{4}\quad {\theta_{1} \cdot \left( {{- I_{1}} + I_{3}} \right)}} + {\sin \frac{3}{4}\quad {\theta_{1} \cdot I_{2}}}} \right\rbrack}} & \left\lbrack {{Expression}\quad 54} \right\rbrack\end{matrix}$

Further, a difference of magnetic field between the synthetic magneticfield of the first hall device 21 and the synthetic magnetic field ofthe second hall device 22 will be obtained. In case of 0<θ₁≦2π/3, thedifference of the magnetic field is expressed by Expression 55.$\begin{matrix}{\begin{matrix}{\frac{1}{4\quad \pi \quad r}\left( {4 + {{3 \cdot \sin}\quad \frac{1}{4}\quad \theta_{1}} - {\sin \quad \frac{3}{4}\quad \theta_{1}}} \right)I_{1}} \\{{\left. 2 \right)\quad {2/3}\quad \pi} \leq \theta_{1} \leq {2\quad \pi}}\end{matrix}} & \left\lbrack {{Expression}\quad 55} \right\rbrack\end{matrix}$

In case of 2π/3≧θ₁≦2π, the difference of the magnetic field is expressedby Expression 56. $\begin{matrix}{\frac{1}{4\quad \pi \quad r}\left( {2 + {{3 \cdot \sin}\quad \frac{1}{4}\quad \theta_{1}} + {\sin \quad \frac{3}{4}\quad \theta_{1}}} \right)I_{1}} & \left\lbrack {{Expression}\quad 56} \right\rbrack\end{matrix}$

If I₁/(4*π*r) is normalized to 1 and a value of the difference of themagnetic field is a function of θ₁, the difference of the magnetic fieldchanges corresponding to changes of θ₁ as shown in FIG. 21. Thisdifference of the magnetic field becomes maximum when θ₁=π.

Next, dividing ratio of the currents I₁, I₂, I₃ are calculated. AssumingI₂/I₁=k, it comes that I₂=kI₁, I₃=−(1+k)I₁ and this k only has to beobtained. First, in case of 0<θ₁≦2π/3, a magnetic field S₁ which thehall device 21 receives is expressed by Expression 57. $\begin{matrix}{S_{1} = {{\frac{1}{4\quad \pi \quad r}\left\lbrack {2 + {\sin \quad \frac{1}{4}\quad \theta_{1}} - {\sin \quad \frac{3}{4}\quad \theta_{1}} + {\left( {{\sin \quad \frac{1}{4}\quad \theta_{1}} + {\sin \quad \frac{3}{4}\quad \theta_{1}}} \right)\kappa}} \right\rbrack}I_{1}}} & \left\lbrack {{Expression}\quad 57} \right\rbrack\end{matrix}$

If it is intended to obtain k by this Expression 57, k is expressed byExpression 58. $\begin{matrix}{\kappa = {- {\frac{1}{{\sin \quad \frac{1}{4}\quad \theta_{1}} + {\sin \quad \frac{3}{4}\quad \theta_{1}}}\left\lbrack {\frac{4\quad \pi \quad r\quad S_{1}}{I_{1}} - \left( {2 + {\sin \quad \frac{1}{4}\quad \theta_{1}} - {\sin \quad \frac{3}{4}\quad \theta_{1}}} \right)} \right\rbrack}}} & \left\lbrack {{Expression}\quad 58} \right\rbrack\end{matrix}$

If magnetic field S₂ received by the hall device 22 is subtracted frommagnetic field S₁ received by the hall device 21, Expression 59 isobtained. $\begin{matrix}{{S_{1} - S_{2}} = {\frac{1}{4\quad \pi \quad r}\left( {4 + {{3 \cdot \sin}\quad \frac{1}{4}\quad \theta_{1}} - {\sin \quad \frac{3}{4}\quad \theta_{1}}} \right)I_{1}}} & \left\lbrack {{Expression}\quad 59} \right\rbrack\end{matrix}$

As a result, the current I₁ is expressed by Expression 60.$\begin{matrix}{I_{1} = \frac{4\quad \pi \quad {r\left( {S_{1} - S_{2}} \right)}}{4 + {3\sin \quad \frac{1}{4}\quad \theta_{1}} - {\sin \quad \frac{3}{4}\quad \theta_{1}}}} & \left\lbrack {{Expression}\quad 60} \right\rbrack\end{matrix}$

If the current I₁ obtained by this Expression 60 is substituted intoExpression 58, k is expressed by Expression 61. $\begin{matrix}{\kappa = {{{- \frac{4 + {3\sin \quad \frac{1}{4}\quad \theta_{1}} - {\sin \quad \frac{3}{4}\quad \theta_{1}}}{{\sin \quad \frac{1}{4}\quad \theta_{1}} + {\sin \quad \frac{3}{4}\quad \theta_{1}}}} \cdot \quad \frac{S_{1}}{S_{1} - S_{2}}} + \quad \frac{2 + {\sin \quad \frac{1}{4}\quad \theta_{1}} - {\sin \quad \frac{3}{4}\quad \theta_{1}}}{{\sin \quad \frac{1}{4}\quad \theta_{1}} + {\sin \quad \frac{3}{4}\quad \theta_{1}}}}} & \left\lbrack {{Expression}\quad 61} \right\rbrack\end{matrix}$

If the branching angle θ₁ is predetermined, the currents I₁, k can beobtained by the magnetic fields S1, S2 which the two hall devices 21, 22receive. By using the obtained k, the currents I₂, I₃ can be obtained.Here, if θ₁=2/3π(θ₁=θ₂=θ₃), k is expressed by Expression 62.$\begin{matrix}{\kappa = {{{- 3}\quad \frac{S_{1}}{S_{1} - S_{2}}} + 1}} & \left\lbrack {{Expression}\quad 62} \right\rbrack\end{matrix}$

By this operation, the currents I₁, I₂, I₃ flowing through threeconductors from magnetic fields received by the two hall devices 21, 22can be obtained.

Next, in case of 2π/3≦θ₁ ≦2π, the magnetic field S ₁ and k are expressedby Expression 63. $\begin{matrix}{{S_{1} = {{- {\frac{1}{4\quad \pi \quad r}\left\lbrack {{\sin \quad \frac{1}{4}\quad \theta_{1}} + {\sin \quad \frac{3}{4}\quad \theta_{1}} + {\left( {{- 2} - {\sin \quad \frac{1}{4}\quad \theta_{1}} + {\sin \quad \frac{3}{4}\quad \theta_{1}}} \right)\kappa}} \right\rbrack}}I_{1}}}{\kappa = {{- \frac{1}{2 + {\sin \quad \frac{1}{4}\quad \theta_{1}} - {\sin \quad \frac{3}{4}\quad \theta_{1}}}}\left( {\frac{4\quad \pi \quad r}{I_{1}} - {\sin \quad \frac{1}{4}\quad \theta_{1}} - {\sin \quad \frac{3}{4}\quad \theta_{1}}} \right)}}} & \left\lbrack {{Expression}\quad 63} \right\rbrack\end{matrix}$

If the magnetic field S2 is subtracted from the magnetic field S₁,Expression 64 is obtained. $\begin{matrix}{{S_{1} - S_{2}} = {\frac{1}{4\quad \pi \quad r}\left( {2 + {3\sin \quad \frac{1}{4}\quad \theta_{1}} + {\sin \quad \frac{3}{4}\quad \theta_{1}}} \right)I_{1}}} & \left\lbrack {{Expression}\quad 64} \right\rbrack\end{matrix}$

The current I₁ is expressed by Expression 65 because of Expression 64.$\begin{matrix}{I_{1} = \frac{4\quad \pi \quad {r\left( {S_{1} - S_{2}} \right)}}{2 + {3\sin \quad \frac{1}{4}\quad \theta_{1}} + {\sin \quad \frac{3}{4}\quad \theta_{1}}}} & \left\lbrack {{Expression}\quad 65} \right\rbrack\end{matrix}$

If the current I₁ of this Expression 65 is substituted into k ofExpression 63, k is expressed by Expression 66. $\begin{matrix}{\kappa = {{{- \frac{2 + {3\sin \quad \frac{1}{4}\quad \theta_{1}} + {\sin \quad \frac{3}{4}\quad \theta_{1}}}{2 + {\sin \quad \frac{1}{4}\quad \theta_{1}} - {\sin \quad \frac{3}{4}\quad \theta_{1}}}} \cdot \quad \frac{S_{1}}{S_{1} - S_{2}}} + \quad \frac{{\sin \quad \frac{1}{4}\quad \theta_{1}} + {\sin \quad \frac{3}{4}\quad \theta_{1}}}{2 + {\sin \quad \frac{1}{4}\quad \theta_{1}} - {\sin \quad \frac{3}{4}\quad \theta_{1}}}}} & \left\lbrack {{Expression}\quad 66} \right\rbrack\end{matrix}$

At angle θ₁=π which maximizes the sensitivity, k is expressed byExpression 67. $\begin{matrix}{\kappa = {{{- \left( {1 + {2\sqrt{2}}} \right)} \cdot \quad \frac{S_{1}}{S_{1} - S_{2}}} + \quad \frac{1}{\sqrt{2}}}} & \left\lbrack {{Expression}\quad 67} \right\rbrack\end{matrix}$

By this operation, the currents I₁, I₂, I₃ flowing through threeconductors from magnetic fields which the two hall devices 21, 22receive can be obtained.

Eleventh Embodiment

According to the eleventh embodiment n of the present invention is “3”and m is “2”. In this example, three angles formed by the branchedfirst-third conductors are different from each other. FIG. 22 is aperspective view showing a structure of the sensor portion of thecurrent detecting apparatus according to the eleventh embodiment of thepresent invention. This sensor portion is comprised of the conductor 10,first hall device 21 and second hall device 22. Usually, thesecomponents are incorporated in an electric connecting box (not shown).In this eleventh embodiment, no magnetism collecting core is employed.

As shown in FIG. 22, the conductor 10 is comprised of the firstconductor 11, second conductor 12 and third conductor 13 disposed inthree directions from the branch point O on a flat plane including thebranch point O. The first conductor 11, second conductor 12 and thethird conductor 13 correspond to n conductors of the present invention.Ends of the respective conductors are connected to the branch point O.

In the meantime, the conductor 10 may be composed by connecting ends ofthe three separate conductors, namely, the first conductor 11, secondconductor 12 and third conductor 13 at the branch point O and instead byforming integrally the first conductor 11, second conductor 12 and thirdconductor 13. Further, it is also permissible to compose this conductor10 by forming a wiring pattern having three branch routes including thefirst conductor 11, second conductor 12 and third conductor 13 on asubstrate.

The first hall device 21 and second hall device 22 correspond to melectromagnetic transducers of the present invention. Each hall devicegenerates a voltage (hall voltage) signal corresponding to a density ofmagnetic flux entering its magnetism sensitive surface (magnetic fluxdetecting surface). A predetermined current is supplied to each halldevice through a lead (not shown) and the voltage signal generated ineach hall device is fetched out through a lead (not shown).

Positions where the respective hall devices are disposed are determinedas follows. That is, the first hall device 21 is disposed between thesecond conductor 12 and the third conductor 13 and at the same distancefrom these conductors. That is, the first hall device 21 is disposed atan angle which divides an angle θ₁ formed by the second conductor 12,branch point O and third conductor 13 to two sections. The second halldevice 22 is disposed between the first conductor 11 and secondconductor 12 and at the same distance from these conductors. That is,the second hall device 22 is disposed at an angle which divides an angleθ₂ formed by the first conductor 11, branch point O and second conductor12 to two sections. For both the hall devices 21, 22, a distance r fromeach of the conductors which sandwich a hall device to the hall deviceis assumed to be equal. Further, the magnetism sensitive surfaces of therespective hall devices substantially coincide with a flat planeincluding the branch point O and are directed in the same direction.

Next, an operation of the sensor portion of the current detectingapparatus according to the eleventh embodiment of the present inventionhaving such a structure will be described.

First, due to Kirchhoff formula, I₁+I₂+I₃=0 and θ₁+θ₂+θ₃=2 π. If r isconsidered to be a constant determined upon design, the variables arethree current values I₁-I₃. Because there are three equations, that is,magnetic fields S₁, S₂ which the hall devices 21, 22 receive andKirchhoff formula, the three variables I₁-I₃ can be determined by twohall devices 21, 22.

Calculation of three variables I₁-I₃ will be described about each casedepending on setting of the angles θ₁, θ₂. First, FIG. 23 shows astructure of the sensor portion in case of 0≦θ₁<2 +θ₂≦π and 0≦θ₁+θ₂/2≦π.A magnetic field which the first hall device 21 receives at this timewill be obtained. First, the magnetic field which the first hall device21 receives from the current I₁ is expressed by Expression 68.$\begin{matrix}{{{- {\frac{1}{4\quad \pi \quad r}\left\lbrack {1 + {\cos \quad \left( {\theta_{2} + {\frac{1}{2}\quad \theta_{1}}} \right)}} \right\rbrack}}I_{1}} = {{{- \frac{1}{4\quad \pi \quad r}}\left( {1 + {\cos \quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{1}} - {\sin \quad {\theta_{2} \cdot \sin}\quad \frac{1}{2}\quad \theta_{1}}} \right)I_{1}} = {{{- {\frac{1}{4\quad \pi \quad r}\left\lbrack {1 + {\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \left( {{2\cos^{2}\quad \frac{1}{2}\quad \theta_{2}} - 1} \right)}} - {2\sin \quad \frac{1}{2}\quad {\theta_{1} \cdot \sin}\quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{2}}} \right\rbrack}}I_{1}} = {{{- {\frac{1}{4\quad \pi \quad r}\left\lbrack {1 - {\cos \quad \frac{1}{2}\quad \theta_{1}} + {2\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{2}} - {\sin \quad \frac{1}{2}\quad {\theta_{1} \cdot \sin}\quad \frac{1}{2}\quad \theta_{2}}} \right)}}} \right\rbrack}}\quad I_{1}} = {{{{- {\frac{1}{4\quad \pi \quad r}\left\lbrack {1 - {\cos \quad \frac{1}{2}\quad \theta_{1}} + {2\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \left( {{\frac{1}{2}\quad \theta_{1}} + {\frac{1}{2}\quad \theta_{2}}} \right)}} \right\rbrack}}\quad I_{1}} = {{{- {\frac{1}{4\quad \pi \quad r}\left\lbrack {1 - {\cos \quad \frac{1}{2}\quad \theta_{1}} + {2\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \left( {\pi - {\frac{1}{2}\quad \theta_{3}}} \right)}} \right\rbrack}}\quad I_{1}} = {{- \frac{1}{4\quad \pi \quad r}}\left( {1 - {\cos \quad \frac{1}{2}\quad \theta_{1}} - {2\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)\quad I_{1}}}}}}}}} & \left\lbrack {{Expression}\quad 68} \right\rbrack\end{matrix}$

The magnetic field which the first hall device 21 receives from thecurrent I₂ is expressed by Expression 69. $\begin{matrix}{{- \frac{1}{4\quad \pi \quad r}}\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)I_{2}} & \left\lbrack {{Expression}\quad 69} \right\rbrack\end{matrix}$

The magnetic field which the first hall device 21 receives from thecurrent I₃ is expressed by Expression 70. $\begin{matrix}{\frac{1}{4\quad \pi \quad r}\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)I_{3}} & \left\lbrack {{Expression}\quad 70} \right\rbrack\end{matrix}$

Thus, the magnetic field which the first hall device 21 receives fromthe currents I₁-I₃ is expressed by Expression 71. $\begin{matrix}{S_{1} = {{\frac{1}{4\quad \pi \quad r}\left\lbrack {{{- \left( {1 - {\cos \quad \frac{1}{2}\quad \theta_{1}} - {2\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\frac{1}{2}\quad \theta_{3}}} \right)}I_{1}} - {\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)I_{2}} + {\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)I_{3}}} \right\rbrack} = {{\frac{1}{4\quad \pi \quad r}\left\lbrack {{- I_{1}} - I_{2} + I_{3} + {\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \left( {I_{1} - I_{2} + I_{3}} \right)}} + {2\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\frac{1}{2}\quad {\theta_{3} \cdot I_{1}}}} \right\rbrack} = {\frac{1}{2\quad \pi \quad r}\left\lbrack {{\left( {{\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\frac{1}{2}\quad \theta_{3}} - 1} \right)I_{1}} - {\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)I_{2}}} \right\rbrack}}}} & \left\lbrack {{Expression}\quad 71} \right\rbrack\end{matrix}$

Next, the magnetic field which the second hall device 22 receives fromthe current I₁ is expressed by Expression 72. $\begin{matrix}{{- \frac{1}{4\quad \pi \quad r}}\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)I_{1}} & \left\lbrack {{Expression}\quad 72} \right\rbrack\end{matrix}$

The magnetic field which the second hall device 22 receives from thecurrent I₂ is expressed by Expression 73. $\begin{matrix}{\frac{1}{4\quad \pi \quad r}\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)I_{2}} & \left\lbrack {{Expression}\quad 73} \right\rbrack\end{matrix}$

The magnetic field which the second hall device 22 receives from thecurrent I₃ is expressed by Expression 74. $\begin{matrix}{\left. {{{\frac{1}{4\quad \pi \quad r}\left\lbrack {1 + {\cos \quad \left( {\theta_{1} + {\frac{1}{2}\quad \theta_{2}}} \right)}} \right\rbrack}I_{3}} = {\frac{1}{4\quad \pi \quad r}\left\lbrack {1 - {\cos \quad \frac{1}{2}\quad \theta_{2}} - {2\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right.}} \right)I_{3}} & \left\lbrack {{Expression}\quad 74} \right\rbrack\end{matrix}$

Therefore, the magnetic field which the second hall device 22 receivesfrom the currents I₁-I₃ is expressed by Expression 75. $\begin{matrix}{S_{2} = {{\frac{1}{4\quad \pi \quad r}\left\lbrack {{{- \left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)}I_{1}} + {\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)I_{2}} + {\left( {1 - {\cos \quad \frac{1}{2}\quad \theta_{2}} - {2\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)I_{3}}} \right\rbrack} = {{\frac{1}{4\quad \pi \quad r}\left( {{{- 2}I_{1}^{\prime}} + {2\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot I_{2}}} - {2\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad {\theta_{3} \cdot I_{3}}}} \right)} = {\frac{1}{2\quad \pi \quad r}\left\lbrack {{\left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)I_{1}} + {\left( {{\cos \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + {\cos \frac{1}{2}\quad \theta_{2}}} \right)I_{2}}} \right\rbrack}}}} & \left\lbrack {{Expression}\quad 75} \right\rbrack\end{matrix}$

Thus, the magnetic fields S₁, S₂ are expressed by Expression 76.$\begin{matrix}\begin{matrix}{{S_{1} = \quad {{\frac{1}{2\quad \pi \quad r}\left\lbrack {{\left( {{\cos \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)I_{1}} - {\left( {1 + {\cos \frac{1}{2}\quad \theta_{1}}} \right)I_{2}}} \right\rbrack}\quad \left( {1 - 3 - 1} \right)}}\quad} \\{S_{2} = \quad {{{\frac{1}{2\quad \pi \quad r}\left\lbrack {\left( {{\cos \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)I_{1}} \right.}} +}} \\{\quad {\left. {{\left( {{\cos \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + {\cos \frac{1}{2}\quad \theta_{2}}} \right)I_{2}}} \right\rbrack \quad \left( {1 - 3 - 2} \right)}}\end{matrix} & \left\lbrack {{Expression}\quad 76} \right\rbrack\end{matrix}$

The current I₁ is expressed by Expression 77 because of (1-3-1) ofequation 76. $\begin{matrix}{{{I_{1} =}}{{\frac{1}{{\cos \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1}{{\left\lbrack {{2\quad \pi \quad r\quad S_{1}} + {\left( {1 + {\cos \frac{1}{2}\quad \theta_{1}}} \right)I_{2}}} \right\rbrack \quad \left( {1 - 3 - 3} \right)}}}}} & \left\lbrack {{Expression}\quad 77} \right\rbrack\end{matrix}$

If this current I₁ is substituted into equation (1-3-2) of Expression76, Expression 78 is obtained. $\begin{matrix}{S_{2} = {{\frac{1}{2\quad \pi \quad r}\left\lbrack \quad {{\frac{{\cos \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1}{{\cos \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \cdot {{{}}\left\lbrack \quad {{2\quad \pi \quad r\quad S_{1}} + \quad {\left( {1 + {\cos \frac{1}{2}\quad \theta_{1}}} \right)I_{2}}} \right\rbrack}} + {\left. {\left( {{\cos \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + {\cos \frac{1}{2}\quad \theta_{2}}} \right)I_{2}} \right\rbrack}} \right.}}} & \left\lbrack {{Expression}\quad 78} \right\rbrack\end{matrix}$

If this Expression 78 is solved with respect to the current I₂,Expression 79 is obtained, so that the current I₂ is obtained.$\begin{matrix}{I_{2} = {\frac{2\quad \pi \quad {r\left\lbrack {{{- \left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)}S_{1}} + {\left( {{\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)S_{2}}} \right\rbrack}}{\begin{matrix}{{\left( {{\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)\quad \left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)} +} \\{\left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)\quad \left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)}\end{matrix}}\quad \text{(1-3-4)}}} & \left\lbrack {{Expression}\quad 79} \right\rbrack\end{matrix}$

Meanwhile, if θ₁=θ₂ is set in the equation (1-3-3), the current I₂ isexpressed by Expression 80. $\begin{matrix}{I_{2} = \frac{2\quad \pi \quad {r\left( {S_{2} - S_{2}} \right)}}{{\frac{1}{2}\sin \quad \frac{3}{4}\quad \theta_{3}} + {\frac{3}{4}\sin \quad \frac{1}{4}\quad \theta_{3}} + 1}} & \left\lbrack {{Expression}\quad 80} \right\rbrack\end{matrix}$

In case where θ₁ is unequal to θ₂ like equation (1-3-4), if two halldevices receive noise having the same level and direction, this noisecannot be canceled by the aforementioned operation. If the equation(1-3-4) is substituted into the equation (1-3-3), the current I₁ isexpressed by Expression 81. $\begin{matrix}\begin{matrix}{I_{1} = \quad \frac{1}{{\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1}} \\{\quad \left\lbrack {{2\quad \pi \quad r\quad S_{1}} + {\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)\quad \frac{2\quad \pi \quad {r\left\lbrack {{\left( {{\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)S_{2}} - {\left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)S_{1}}} \right\rbrack}}{{\left( {{\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)\quad \left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)} + {\left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)\quad \left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)}}}} \right\rbrack} \\{= \quad {\frac{2\quad \pi \quad {r\left\lbrack {{\left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)S_{1}} + {\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)S_{2}}} \right\rbrack}}{{\left( {{\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)\quad \left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)} + {\left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)\quad \left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)}}\quad \text{(1-3-5)}}}\end{matrix} & \left\lbrack {{Expression}\quad 81} \right\rbrack\end{matrix}$

Further, the current I₃ is obtained due to Kirchhoff formula and thiscurrent I₃ is expressed by Expression 82. $\begin{matrix}\begin{matrix}{I_{3} = \quad {{- I_{1}} - I_{2}}} \\{= \quad \frac{{{- 2}\quad \pi \quad {r\left\lbrack {{\left( {{\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)S_{2}} - {\left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)S_{1}}} \right\rbrack}} - {2\quad \pi \quad {r\left\lbrack {{\left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)S_{1}} + {\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)S_{2}}} \right\rbrack}}}{{\left( {{\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)\quad \left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)} + {\left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)\quad \left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)}}} \\{= \quad {\frac{{- 2}\quad \pi \quad {r\left\lbrack {{\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)S_{1}} + {\left( {{\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)S_{2}}} \right\rbrack}}{{\left( {{\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)\quad \left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)} + {\left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)\quad \left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)}}\quad \text{(1-3-6)}}}\end{matrix} & \left\lbrack {{Expression}\quad 82} \right\rbrack\end{matrix}$

Next, FIG. 24 shows a structure of the sensor portion in case of π≦θ₁/2+θ₂≦2π and 0≦θ₁+θ₂/2≦π. A magnetic field which the first hall device 21receives in this case is obtain. First, the magnetic field which thefirst hall device 21 from the current I₁ is expressed by Expression 83.$\begin{matrix}{{{- {\frac{1}{4\quad \pi \quad r}\left\lbrack {1 + {\cos \quad \left( {\theta_{2} + {\frac{1}{2}\quad \theta_{1}}} \right)}} \right\rbrack}}\quad I_{1}} = {\frac{1}{4\quad \pi \quad r}\left( {1 - {\cos \quad \frac{1}{2}\quad \theta_{1}} - {2\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)I_{1}}} & \left\lbrack {{Expression}\quad 83} \right\rbrack\end{matrix}$

The magnetic field which the first hall device 21 receives from thecurrent I₂ is expressed by Expression 84. $\begin{matrix}{{- \frac{1}{4\quad \pi \quad r}}\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)\quad I_{2}} & \left\lbrack {{Expression}\quad 84} \right\rbrack\end{matrix}$

The magnetic field which the first hall device 21 receives from thecurrent I₃ is expressed by Expression 85. $\begin{matrix}{\frac{1}{4\quad \pi \quad r}\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)\quad I_{3}} & \left\lbrack {{Expression}\quad 85} \right\rbrack\end{matrix}$

Thus, a magnetic field which the first hall device 21 from the currentsI₁-I₃ is expressed by Expression 86. $\begin{matrix}{S_{1} = {{\frac{1}{4\quad \pi \quad r}\left\lbrack {{\left( {1 - {\cos \quad \frac{1}{2}\quad \theta_{1}} - {2\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)I_{1}} - {\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)I_{2}} + {\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)I_{3}}} \right\rbrack} = {\frac{1}{2\quad \pi \quad r}\left\lbrack {{\left( {{{- \cos}\quad \frac{1}{2}\quad \theta_{1}} - {\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)I_{1}} + {\left( {{- 1} - {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)I_{2}}} \right\rbrack}}} & \left\lbrack {{Expression}\quad 86} \right\rbrack\end{matrix}$

Next, the magnetic field which the second hall device 22 receives fromthe current I₁ is expressed by Expression 87. $\begin{matrix}{{- \frac{1}{4\quad \pi \quad r}}\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)I_{1}} & \left\lbrack {{Expression}\quad 87} \right\rbrack\end{matrix}$

The magnetic field which the second hall device 22 receives from thecurrent I₂ is expressed by Expression 88. $\begin{matrix}{\frac{1}{4\quad \pi \quad r}\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)I_{2}} & \left\lbrack {{Expression}\quad 88} \right\rbrack\end{matrix}$

The magnetic field which the second hall device 22 receives from thecurrent I₃ is expressed by Expression 89. $\begin{matrix}{{{\frac{1}{4\quad \pi \quad r}\left\lbrack {1 + {\cos \quad \left( {\theta_{1} + {\frac{1}{2}\quad \theta_{2}}} \right)}} \right\rbrack}\quad I_{3}} = {\frac{1}{4\quad \pi \quad r}\left( {1 - {\cos \quad \frac{1}{2}\quad \theta_{2}} - {2\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)I_{3}}} & \left\lbrack {{Expression}\quad 89} \right\rbrack\end{matrix}$

Therefore, the magnetic field which the second hall device receives frome currents I₁-I₃ is expressed by Expression 90. $\begin{matrix}{S_{2} = {{\frac{1}{4\quad \pi \quad r}\left\lbrack {{{- \left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)}I_{1}} + {\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)I_{2}} + {\left( {1 - {\cos \quad \frac{1}{2}\quad \theta_{2}} - {2\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)I_{3}}} \right\rbrack} = {\frac{1}{2\quad \pi \quad r}\left\lbrack {{\left( {{- 1} - {\cos \quad \frac{1}{2}\quad \theta_{2}} + {\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)I_{1}} + {\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad {\theta_{3} \cdot I_{2}}}} \right\rbrack}}} & \left\lbrack {{Expression}\quad 90} \right\rbrack\end{matrix}$

Therefore, the magnetic fields S₁, S₂ are expressed by Expression 91.$\begin{matrix}{{S_{1} = {{\frac{1}{2\quad \pi \quad r}\left\lbrack {{\left( {{{- \cos}\quad \frac{1}{2}\quad \theta_{1}} - {\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)I_{1}} + {\left( {1 - {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)I_{2}}} \right\rbrack}\quad \text{(2-3-1)}}}{S_{2} = {{\frac{1}{2\quad \pi \quad r}\left\lbrack {{\left( {{- 1} - {\cos \quad \frac{1}{2}\quad \theta_{2}} + {\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)I_{1}} + {\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad {\theta_{3} \cdot I_{2}}}} \right\rbrack}\quad \text{(2-3-2)}}}} & \left\lbrack {{Expression}\quad 91} \right\rbrack\end{matrix}$

The current I₂ is expressed by Expression 92 because of the equation(2-3-2) of Expression 91. $\begin{matrix}{I_{2} = {{\frac{1}{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}\left\lbrack {{2\quad \pi \quad r\quad S_{2}} + {\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{2}} - {\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)I_{1}}} \right\rbrack}\quad \text{(2-3-3)}}} & \left\lbrack {{Expression}\quad 92} \right\rbrack\end{matrix}$

If the current I₂ is substituted into the equation (2-3-1) of Expression91, Expression 93 is obtained, and thus, the current I₁ is obtained.$\begin{matrix}{I_{1} = {\frac{2\quad \pi \quad {r\left\lbrack {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad {\theta_{3} \cdot S_{1}}} + {\left( {{\cos \quad \frac{1}{2}\quad \theta_{1}} + 1} \right)S_{2}}} \right\rbrack}}{\begin{matrix}{{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad {\theta_{3} \cdot \left( {{{- \cos}\quad \frac{1}{2}\quad \theta_{1}} - {\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)}} +} \\{\left( {{- 1} - {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)\left( {{\cos \quad \frac{1}{2}\quad \theta_{2}} - {\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + 1} \right)}\end{matrix}}\quad \text{(2-3-4)}}} & \left\lbrack {{Expression}\quad 93} \right\rbrack\end{matrix}$

If this expression 93 is substituted into the equation (2-3-3),Expression 94 is obtained, and thus the current I₂ and current I₃ areobtained. $\begin{matrix}\begin{matrix}{I_{2} = \quad {\frac{2\quad \pi \quad {r\left\lbrack {{\left( {{\cos \quad \frac{1}{2}\quad \theta_{2}} - {\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + 1} \right)S_{1}} + {\left( {{{- \cos}\quad \frac{1}{2}\quad \theta_{1}} - {\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)S_{2}}} \right\rbrack}}{{{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad {\theta_{3} \cdot \left( {{{- \cos}\quad \frac{1}{2}\quad \theta_{1}} - {\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)}} + {\left( {{- 1} - {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)\quad \left( {{\cos \quad \frac{1}{2}\quad \theta_{2}} - {\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + 1} \right)}}\quad}\quad \text{(2-3-5)}}} \\{I_{3} = \quad {{- I_{1}} - I_{2}}} \\{= \quad {\frac{2\quad \pi \quad {r\left\lbrack {{\left( {{{- \cos}\quad \frac{1}{2}\quad \theta_{2}} - 1} \right)S_{1}} + {\left( {{\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + 1} \right)S_{2}}} \right\rbrack}}{{{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad {\theta_{3} \cdot \left( {{{- \cos}\quad \frac{1}{2}\quad \theta_{1}} - {\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)}} + {\left( {{- 1} - {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)\quad \left( {{\cos \quad \frac{1}{2}\quad \theta_{2}} - {\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + 1} \right)}}\quad}\quad \text{(2-3-6)}}}\end{matrix} & \left\lbrack {{Expression}\quad 94} \right\rbrack\end{matrix}$

Next, FIG. 25 shows a structure of the sensor portion in case ofπ≦θ₁/2+θ₂≦2π and π≦θ₁+θ₂/2≦2π. A magnetic field which the first halldevice 21 receives in this case is obtained. First, the magnetic fieldwhich the first hall device 21 from the current I₁ is expressed byExpression 95. $\begin{matrix}{{{\frac{1}{4\quad \pi \quad r}\left\lbrack {1 + {\cos \quad \left( {\theta_{2} + {\frac{1}{2}\quad \theta_{1}}} \right)}} \right\rbrack}\quad I_{1}} = {\frac{1}{4\quad \pi \quad r}\left( {1 - {\cos \quad \frac{1}{2}\quad \theta_{1}} - {2\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)I_{1}}} & \left\lbrack {{Expression}\quad 95} \right\rbrack\end{matrix}$

The magnetic field which the first hall device 21 receives from thecurrent I₂ is expressed by Expression 96. $\begin{matrix}{{- \frac{1}{4\quad \pi \quad r}}\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)I_{2}} & \left\lbrack {{Expression}\quad 96} \right\rbrack\end{matrix}$

The magnetic field which the first hall device 21 receives from thecurrent I₃ is expressed by Expression 97. $\begin{matrix}{\frac{1}{4\quad \pi \quad r}\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)I_{3}} & \left\lbrack {{Expression}\quad 97} \right\rbrack\end{matrix}$

Therefore, the magnetic field which the first hall device 21 receivesfrom the currents I₁-I₃ is expressed by Expression 98. $\begin{matrix}{S_{1} = {{\frac{1}{4\quad \pi \quad r}\left\lbrack {{\left( {1 - {\cos \quad \frac{1}{2}\quad \theta_{1}} - {2\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)I_{1}} - {\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)I_{2}} + {\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)I_{3}}} \right\rbrack} = {\frac{1}{2\quad \pi \quad r}\left\lbrack {{\left( {{{- \cos}\quad \frac{1}{2}\quad \theta_{1}} - {\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)I_{1}} + {\left( {{- 1} - {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)I_{2}}} \right\rbrack}}} & \left\lbrack {{Expression}\quad 98} \right\rbrack\end{matrix}$

Next, the magnetic field which the second hall device 22 receives fromthe current I₁ is expressed by Expression 99. $\begin{matrix}{{- \frac{1}{4\quad \pi \quad r}}\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)I_{1}} & \left\lbrack {{Expression}\quad 99} \right\rbrack\end{matrix}$

The magnetic field which the second hall device receives from thecurrent I₂ is expressed by Expression 100. $\begin{matrix}{\frac{1}{4\quad \pi \quad r}\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)I_{2}} & \left\lbrack {{Expression}\quad 100} \right\rbrack\end{matrix}$

The magnetic field which the second hall device 22 receives from thecurrent I₃ is expressed by Expression 101. $\begin{matrix}{{{- {\frac{1}{4\quad \pi \quad r}\left\lbrack {1 + {\cos \quad \left( {\theta_{1} + {\frac{1}{2}\quad \theta_{2}}} \right)}} \right\rbrack}}\quad I_{3}} = {{- \frac{1}{4\quad \pi \quad r}}\left( {1 - {\cos \quad \frac{1}{2}\quad \theta_{2}} - {2\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)I_{3}}} & \left\lbrack {{Expression}\quad 101} \right\rbrack\end{matrix}$

Therefore, the magnetic field which the second hall device 22 receivesfrom the currents I₁-I₃ is expressed by Expression 102. $\begin{matrix}{S_{2} = {{\frac{1}{4\quad \pi \quad r}\left\lbrack {{{- \left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)}I_{1}} + {\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)I_{2}} - {\left( {1 - {\cos \quad \frac{1}{2}\quad \theta_{2}} - {2\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)I_{3}}} \right\rbrack} = {\frac{1}{2\quad \pi \quad r}\left\lbrack {{\left( {{{- \cos}\quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)I_{1}} + {\left( {1 - {\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)I_{2}}} \right\rbrack}}} & \left\lbrack {{Expression}\quad 102} \right\rbrack\end{matrix}$

Thus, the magnetic fields S₁, S₂ are expressed by Expression 103.$\begin{matrix}{{S_{1} = {{\frac{1}{2\quad \pi \quad r}\left\lbrack {{\left( {{{- \cos}\quad \frac{1}{2}\quad \theta_{1}} - {\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)I_{1}} + {\left( {{- 1} - {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)I_{2}}} \right\rbrack}\quad \text{(3-3-1)}}}{S_{2} = {{{\frac{1}{2\quad \pi \quad r}\left\lbrack {{\left( {{{- \cos}\quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)I_{1}} + {\left( {1 - {\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)I_{2}}} \right\rbrack}\quad \text{(3-3-2)}}}}} & \left\lbrack {{Expression}\quad 103} \right\rbrack\end{matrix}$

Due to the equation (3-3-2) of Expression 103, the current I₂ isexpressed by Expression 104. $\begin{matrix}{I_{2} = {\frac{1}{1 - {\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}}{{\left\lbrack \quad {{2\quad \pi \quad r\quad S_{2}} + {\left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)I_{1}}} \right\rbrack \quad \text{(3-3-3)}}}}} & \left\lbrack {{Expression}\quad 104} \right\rbrack\end{matrix}$

If this current I₂ is substituted into the equation (3-3-1) ofExpression 103, Expression 105 is obtained and thus, the current I₁ isobtained. $\begin{matrix}{I_{1} = {\frac{2\quad \pi \quad {r\left\lbrack {{\left( {1 - {\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)S_{1}} + {\left( {{\cos \quad \frac{1}{2}\quad \theta_{1}} + 1} \right)S_{2}}} \right\rbrack}}{\begin{matrix}{{\left( {1 - {\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)\quad \left( {{{- \cos}\quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)} +} \\{\left( {{- 1} - {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)\quad \left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)}\end{matrix}\quad}\quad \text{(3-3-4)}}} & \left\lbrack {{Expression}\quad 105} \right\rbrack\end{matrix}$

If this expression 105 is substituted into the equation (3-3-3),Expression 106 is obtained and then, the currents I₂, I₃ are obtained.$\begin{matrix}\begin{matrix}{I_{2} = \quad {\frac{2\quad \pi \quad {r\left\lbrack {{\left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)S_{1}} + {\left( {{{- \cos}\quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)S_{2}}} \right\rbrack}}{{{\left( {1 - {\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)\quad \left( {{{- \cos}\quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)} + {\left( {{- 1} - {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)\quad \left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)}}\quad}\quad \text{(3-3-5)}}} \\{I_{3} = \quad {{- I_{1}} - I_{2}}} \\{= \quad {\frac{2\quad \pi \quad {r\left\lbrack {{\left( {{{- \cos}\quad \frac{1}{2}\quad \theta_{2}} - 1} \right)S_{1}} + {\left( {{{- \cos}\quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)S_{2}}} \right\rbrack}}{{{\left( {1 - {\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)\quad \left( {{{- \cos}\quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)} + {\left( {{- 1} - {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)\quad \left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)}}\quad}\quad \text{(3-3-6)}}}\end{matrix} & \left\lbrack {{Expression}\quad 106} \right\rbrack\end{matrix}$

Here, θ₁=θ₂ is set to the equation (3-3-5) and the current I₂ flowingthrough a conductor sandwiched by the two hall devices 21, 22 isexpressed by Expression 107. $\begin{matrix}{I_{2} = \frac{2\quad \pi \quad r\quad \left( {S_{2} - S_{1}} \right)}{\left( {2 + {\frac{3}{2}\sin \quad \frac{1}{4}\quad \theta_{3}} - {\frac{1}{2}\sin \quad \frac{3}{4}\quad \theta_{3}}} \right)}} & \left\lbrack {{Expression}\quad 107} \right\rbrack\end{matrix}$

Next, FIG. 26 shows a structure of the sensor portion in case ofπ≦θ₁/2+θ₂≦π and π≦θ₁+θ₂/2≦2π. A magnetic field which the first halldevice 21 receives in this case will be obtained. First, the magneticfield which the first hall device 21 from the current I₁ is expressed byExpression 108. $\begin{matrix}{{{- {\frac{1}{4\quad \pi \quad r}\left\lbrack {1 + {\cos \quad \left( {\theta_{2} + {\frac{1}{2}\quad \theta_{1}}} \right)}} \right\rbrack}}\quad I_{1}} = {{- \frac{1}{4\quad \pi \quad r}}\left( {1 - {\cos \quad \frac{1}{2}\quad \theta_{1}} - {2\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)I_{1}}} & \left\lbrack {{Expression}\quad 108} \right\rbrack\end{matrix}$

The magnetic field which the first hall device 21 receives from thecurrent I₂ is expressed by Expression 109. $\begin{matrix}{{- \frac{1}{4\quad \pi \quad r}}\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)I_{2}} & \left\lbrack {{Expression}\quad 109} \right\rbrack\end{matrix}$

The magnetic field which the first hall device 21 receives from thecurrent I₃ is expressed by Expression 110. $\begin{matrix}{\frac{1}{4\quad \pi \quad r}\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)I_{3}} & \left\lbrack {{Expression}\quad 110} \right\rbrack\end{matrix}$

Therefore, the magnetic field which the first hall device 21 receivesfrom the currents I₁-I₃ is expressed by Expression 111. $\begin{matrix}{S_{1} = {{\frac{1}{4\quad \pi \quad r}\left\lbrack {{{- \left( {1 - {\cos \quad \frac{1}{2}\quad \theta_{1}} - {2\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}}} \right)}I_{1}} - {\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)I_{2}} + {\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)I_{3}}} \right\rbrack} = {\frac{1}{2\quad \pi \quad r}\left\lbrack \quad {{\left( {{{- \cos}\quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)I_{1}} + {\left( {{{- \cos}\quad \frac{1}{2}\quad \theta_{1}} - 1} \right)I_{2}}} \right\rbrack}}} & \left\lbrack {{Expression}\quad 111} \right\rbrack\end{matrix}$

Next, the magnetic field which the second hall device 22 receives fromthe current I₁ is expressed by Expression 112. $\begin{matrix}{{- \frac{1}{4\quad \pi \quad r}}\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)I_{1}} & \left\lbrack {{Expression}\quad 112} \right\rbrack\end{matrix}$

The magnetic field which the second hall device 22 receives from thecurrent I₂ is expressed by Expression 113. $\begin{matrix}{\frac{1}{4\quad \pi \quad r}\left( {1 + {\cos \quad \frac{1}{2}\theta_{2}}} \right)I_{2}} & \left\lbrack {{Expression}\quad 113} \right\rbrack\end{matrix}$

The magnetic field which the second hall device 22 receives from thecurrent I₃ is expressed by Expression 114. $\begin{matrix}{{{- {\frac{1}{4\quad \pi \quad r}\left\lbrack {1 + {\cos \quad \left( {\theta_{1} + {\frac{1}{2}\theta_{2}}} \right)}} \right\rbrack}}I_{3}} = {\left. {- {\frac{1}{4\quad \pi \quad r}\left\lbrack {1 - {\cos \quad \frac{1}{2}\theta_{2}} - {2\cos \quad \frac{1}{2}{\theta_{1} \cdot \cos}\quad \frac{1}{2}\theta_{3}}} \right.}} \right)I_{3}}} & \left\lbrack {{Expression}\quad 114} \right\rbrack\end{matrix}$

Thus, the magnetic field which the second hall device receives from thecurrents I₁-I₃ is expressed by Expression 115. $\begin{matrix}{S_{2} = {{\frac{1}{4\quad \pi \quad r}\left\lbrack {{{- \left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)}I_{1}} + {\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)I_{2}} - {\left( {1 - {\cos \quad \frac{1}{2}\quad \theta_{2}} - {2\cos \quad \frac{1}{2}{\theta_{1} \cdot \cos}\quad \frac{1}{2}\theta_{3}}} \right)I_{3}}} \right\rbrack} = {\frac{1}{2\quad \pi \quad r}\left\lbrack \quad {{\left( {{{- \cos}\quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)I_{1}} + {\left( {1 - {\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\theta_{3}}} \right)I_{2}}} \right\rbrack}}} & \left\lbrack {{Expression}\quad 115} \right\rbrack\end{matrix}$

Thus, the magnetic fields S₁, S₂ are expressed by Expression 116.$\begin{matrix}{{S_{1} = {{\frac{1}{2\quad \pi \quad r}\left\lbrack {{\left( {{\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\theta_{3}} - 1} \right)I_{1}} - {\left( {1 + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)I_{2}}} \right\rbrack}\quad \text{(4-3-1)}}}{S_{2} = {{\frac{1}{2\quad \pi \quad r}\left\lbrack {{\left( {{{- \cos}\quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\theta_{3}} - {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)I_{1}} + {\left( {1 - {\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\theta_{3}}} \right)I_{2}}} \right\rbrack}\quad \text{(4-3-2)}}}} & \left\lbrack {{Expression}\quad 116} \right\rbrack\end{matrix}$

The current I₁ is expressed by Expression 117 because of the equation(4-3-1) of Expression 116. $\begin{matrix}{I_{1} = {{{\frac{1}{{\cos \quad \frac{1}{2}{\theta_{2} \cdot \cos}\quad \frac{1}{2}\theta_{3}} - 1}\left\lbrack \quad {{2\quad \pi \quad r\quad S_{1}} + {\left( {1 + {\cos \quad \frac{1}{2}\theta_{1}}} \right)I_{2}}} \right\rbrack}\quad \text{(4-3-3)}}}} & \left\lbrack {{Expression}\quad 117} \right\rbrack\end{matrix}$

If this current I₁ is substituted into the equation (4-3-2) ofExpression 116, Expression 118 is obtained and thus the current I₂ isobtained. $\begin{matrix}{I_{2} = {\frac{2\quad \pi \quad {r\left\lbrack {{\left( {{\cos \quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + {\cos \quad \frac{1}{2}\theta_{2}}} \right)S_{1}} + {\left( {{\cos \quad \frac{1}{2}{\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)S_{2}}} \right\rbrack}}{\begin{matrix}{{\left( {{{- \cos}\quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - {\cos \quad \frac{1}{2}\theta_{2}}} \right)\quad \left( {{\cos \quad \frac{1}{2}\quad \theta_{1}} + 1} \right)} +} \\{\left( {{{- \cos}\quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + 1} \right)\quad \left( {{\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)}\end{matrix}}\quad \text{(4-3-4)}}} & \left\lbrack {{Expression}\quad 118} \right\rbrack\end{matrix}$

If this expression 118 is substituted into the equation (4-3-3),Expression 119 is obtained and thus the current I₁ is obtained.$\begin{matrix}{I_{1} = {\frac{2\quad \pi \quad {r\left\lbrack {{\left( {{{- \cos}\quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + 1} \right)S_{1}} + {\left( {{\cos \quad \frac{1}{2}\theta_{1}} + 1} \right)S_{2}}} \right\rbrack}}{\begin{matrix}{{\left( {{{- \cos}\quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - {\cos \quad \frac{1}{2}\theta_{2}}} \right)\quad \left( {{\cos \quad \frac{1}{2}\quad \theta_{1}} + 1} \right)} +} \\{\left( {{{- \cos}\quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + 1} \right)\quad \left( {{\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)}\end{matrix}}\quad \text{(4-3-5)}}} & \left\lbrack {{Expression}\quad 119} \right\rbrack\end{matrix}$

Further, the current I₃ is obtained because of Kirchhoff formula and thecurrent I₃ is expressed by Expression 120. $\begin{matrix}\begin{matrix}{I_{3} = \quad {{- I_{1}} - I_{2}}} \\{= \quad {\frac{{- 2}\quad \pi \quad {r\left\lbrack {{\left( {{\cos \quad \frac{1}{2}\quad \theta_{2}} + 1} \right)S_{1}} + {\left( {{\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + {\cos \quad \frac{1}{2}\quad \theta_{1}}} \right)S_{2}}} \right\rbrack}}{\begin{matrix}{{\left( {{{- \cos}\quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - {\cos \quad \frac{1}{2}\quad \theta_{2}}} \right)\quad \left( {{\cos \quad \frac{1}{2}\quad \theta_{1}} + 1} \right)} +} \\{\left( {{{- \cos}\quad \frac{1}{2}\quad {\theta_{1} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} + 1} \right)\quad \left( {{\cos \quad \frac{1}{2}\quad {\theta_{2} \cdot \cos}\quad \frac{1}{2}\quad \theta_{3}} - 1} \right)}\end{matrix}\quad}\quad \text{(4-3-6)}}}\end{matrix} & \left\lbrack {{Expression}\quad 120} \right\rbrack\end{matrix}$

What is claimed is:
 1. A current detecting apparatus comprising: nconductors disposed so as to be branched radially from a branch point; melectromagnetic transducers disposed between adjacent conductors of saidn conductors; and an operation processing circuit for detecting acurrent flowing through each of said n conductors based on an operatingoutput obtained from a predetermined operation based on an electricsignal from each of said m electromagnetic transducers,  wherein n:integer satisfying n≧3 m: integer satisfying m≧2.
 2. A current detectingapparatus according to claim 1 wherein said n conductors are disposed ona flat plane including said branch point and said m electromagnetictransducers are disposed such that a magnetism sensitive surface of eachthereof exists on said flat plane.
 3. A current detecting apparatusaccording to claim 2 wherein said n is “3” while the three conductorsare disposed every 120° from the branch point on said flat plane inthree directions; said m is “3” while the three electromagnetictransducers are disposed at the same distance from adjacent conductorsand at the same distance from said branch point; and said operationprocessing circuit detects a current flowing through the conductor byobtaining a difference of electric signal between the twoelectromagnetic transducers sandwiching each conductor.
 4. A currentdetecting apparatus according to claim 3 wherein said m electromagnetictransducers are disposed such that the magnetism sensitive surfacesthereof are directed in the same direction.
 5. A current detectingapparatus according to claim 2 where said n is “3” while the threeconductors are disposed in three directions from the branch point onsaid flat plane such that an angle between the first conductor and thesecond conductor is 90°, an angle between the second conductor and thethird conductor is 90° and an angle between the third conductor and thefirst conductor is 180°; said m is “4” while the first electromagnetictransducer is disposed at the same distance from the first conductor andthe second conductor and at the same distance from said branch point,the second electromagnetic transducer is disposed at the same distancefrom the second conductor and the third conductor and at the samedistance from said branch point, the third electromagnetic transducer isdisposed symmetrically with the second electromagnetic transducer withrespect to the third conductor and at the same distance from said branchpoint, and the fourth electromagnetic transducer is disposedsymmetrically with the first electromagnetic transducer with respect tothe first conductor and at the same distance from said branch point;said operation processing circuit detects a current flowing through saidconductor by obtaining a difference of electric signal between the fourelectromagnetic transducers sandwiching each conductor.
 6. A currentdetecting apparatus according to claim 2 wherein said n is “4” while thefour conductors are disposed every 90° from the branch point on saidflat plane in four direction; said m is “4” while the fourelectromagnetic transducers are disposed at the same distance fromadjacent two conductors and at the same distance from said branch point;and said operation processing circuit detects a current flowing throughsaid conductor by obtaining a difference of electric signal among thefour electromagnetic transducers sandwiching each conductor.
 7. Acurrent detecting apparatus according to claim 1 wherein said nconductors are disposed on three-dimensional axes perpendicular to eachother with said branch point as a home position and said melectromagnetic transducers are disposed such that magnetism sensitivesurfaces thereof exist on a flat plane including two axes of said threeaxes.
 8. A current detecting apparatus according to claim 7 wherein saidn is “3” while the three conductors are disposed in three directions ofsaid three axes; said m is “3” while the first electromagnetictransducer is disposed at the same distance from the first conductor andthe second conductor existing on said flat plane and at the samedistance from said branch point, the second electromagnetic transduceris disposed symmetrically with the first electromagnetic transducer withrespect to the second conductor and at the same distance from saidbranch point and the third electromagnetic transducer is disposedsymmetrically with the first electromagnetic transducer with respect tothe first conductor and at the same distance from said branch point; andsaid operation processing circuit detects a current flowing through eachconductor of the first-third conductor by obtaining a difference ofelectric signal between three electromagnetic transducers sandwichingeach of the first conductor and the second conductor existing on saidflat plane.
 9. A current detecting apparatus according to claim 7wherein said n is “4” while the four conductors are disposed on saidthree axes and a negative direction axis of one of said three axes; saidm is “4” while the first-fourth electromagnetic transducers are disposedon a flat plane including two axes of said three axes and said negativedirection axes; said first electromagnetic transducer and said secondelectromagnetic transducer are disposed at the same distance from thefirst conductor which is one of the first-third conductors existing onsaid flat plane and at the same distance from said branch point, thethird electromagnetic transducer is disposed symmetrically with thesecond electromagnetic transducer with respect to the second conductorand at the same distance from said branch point, and the fourthelectromagnetic transducer is disposed symmetrically with the thirdelectromagnetic transducer with respect to the third conductor and atthe same distance from said branch point; and said operation processingcircuit detects a current flowing through each conductor of thefirst-fourth conductors by obtaining a difference of electric signalbetween the four electromagnetic transducers sandwiching each conductorof said first-third conductors existing on said flat plane.
 10. Acurrent detecting method comprising: disposing n conductors so as to bebranched radially from a branch point; disposing m electromagnetictransducers between adjacent conductors of said n conductors; anddetecting a current flowing through each of said n conductors based onan operating output obtained from a predetermined operation based on anelectric signal from each of said m electromagnetic transducers, wherein n: integer satisfying n≧3 m: integer satisfying m≧2.
 11. Acurrent detecting method according to claim 10 wherein said n conductorsare disposed on a flat plane including said branch point and said melectromagnetic transducers are disposed such that a magnetism sensitivesurface of each thereof exists on said flat plane.
 12. A currentdetecting method according to claim 11 comprising: while said n is “3”,disposing the three conductors every 120° from the branch point on saidflat plane in three directions; while said m is “3”, disposing the threeelectromagnetic transducers at the same distance from adjacentconductors and at the same distance from said branch point; anddetecting a current flowing through the conductor by obtaining adifference of electric signal between the two electromagnetictransducers sandwiching each conductor.
 13. A current detecting methodaccording to claim 12 wherein said m electromagnetic transducers aredisposed such that the magnetism sensitive surfaces thereof are directedin the same direction.
 14. A current detecting method according to claim11 comprising: while said n is “3”, disposing the three conductors inthree directions from the branch point on said flat plane such that anangle between the first conductor and the second conductor is 90°, anangle between the second conductor and the third conductor is 90° and anangle between the third conductor and the first conductor is 180°; whilesaid m is “4”, disposing the first electromagnetic transducer at thesame distance from the first conductor and the second conductor and atthe same distance from said branch point, disposing the secondelectromagnetic transducer at the same distance from the secondconductor and the third conductor and at the same distance from saidbranch point, disposing the third electromagnetic transducersymmetrically with the second electromagnetic transducer with respect tothe third conductor and at the same distance from said branch point, anddisposing the fourth electromagnetic transducer symmetrically with thefirst electromagnetic transducer with respect to the first conductor andat the same distance from said branch point; and detecting a currentflowing through said conductor by obtaining a difference of electricsignal between the four electromagnetic transducers sandwiching eachconductor.
 15. A current detecting method according to claim 11 whereinsaid n is “4” while the four conductors are disposed every 90° from thebranch point on said flat plane in four direction; said m is “4” whilethe four electromagnetic transducers are disposed at the same distancefrom adjacent two conductors and at the same distance from said branchpoint; and a current flowing through said conductor is detected byobtaining a difference of electric signal among the four electromagnetictransducers sandwiching each conductor.
 16. A current detecting methodaccording to claim 10 wherein said n conductors are disposed onthree-dimensional axes perpendicular to each other with said branchpoint as a home position and said m electromagnetic transducers aredisposed such that magnetism sensitive surfaces thereof exist on a flatplane including two axes of said three axes.
 17. A current detectingmethod according to claim 16 wherein said n is “3” while the threeconductors are disposed in three directions of said three axes; said mis “3” while the first electromagnetic transducer is disposed at thesame distance from the first conductor and the second conductor existingon said flat plane and at the same distance from said branch point, thesecond electromagnetic transducer is disposed symmetrically with thefirst electromagnetic transducer with respect to the second conductorand at the same distance from said branch point and the thirdelectromagnetic transducer is disposed symmetrically with the firstelectromagnetic transducer with respect to the first conductor and atthe same distance from said branch point; and a current flowing througheach conductor of the first-third conductor is detected by obtaining adifference of electric signal between three electromagnetic transducerssandwiching each of the first conductor and the second conductorexisting on said flat plane.
 18. A current detecting method according toclaim 16 wherein said n is “4” while the four conductors are disposed onsaid three axes and a negative direction axis of one of said three axes;said m is “4” while the first-fourth electromagnetic transducers aredisposed on a flat plane including two axes of said three axes and saidnegative direction axes; said first electromagnetic transducer and saidsecond electromagnetic transducer are disposed at the same distance fromthe first conductor which is one of the first-third conductors existingon said flat plane and at the same distance from said branch point, thethird electromagnetic transducer is disposed symmetrically with thesecond electromagnetic transducer with respect to the second conductorand at the same distance from said branch point, and the fourthelectromagnetic transducer is disposed symmetrically with the thirdelectromagnetic transducer with respect to the third conductor and atthe same distance from said branch point; and a current flowing througheach conductor of the first-fourth conductors is detected by obtaining adifference of electric signal between the four electromagnetictransducers sandwiching each conductor of said first-third conductorsexisting on said flat plane.